This teacher takes his time and explains each step very clearly. So, stop saying he talks too much and to hurry up. No, if you're bored with his teaching, just move on and leave his page.
We're not saying he talks too much. We are saying that the seeming tangents he sometimes goes off on are both distracting and not germain to the solution. In spite of this, I enjoy his explanations.
@@1975KyleDavid My math is different than yours. In the premise, Dan is 6 years older than Ann. ….if he’s 10 and suppose to be twice her age, that means Ann is 5. Can’t be… when he suppose to be twice her age...and 6 years older. Her 5 and he’s 10 doesn’t add up to 6 years older.
@@1975KyleDavid I was wrong...and do the explaining for you...If Dan is 10 now…. in two yrs he will be 12 And in the those two years in the future, Ann’s age would be 6…two years ago she was 4 When Ann was 4 and Dan 6years older .. that would make him 10 now. Dan is now 10 in two years he will be 12, and Ann will be 6….meaning Dan would be twice Ann’s age… she being 6. A heck of a mind twister!
I love your videos. You explain math in very easy terms! I was in honors math in high school but forgot a lot of it in the last 50 years, but you make it easy to bring it all back.
No need for any equations. Start from the possible answers. Pick any one. It takes just a moment to see if it is too high, too low, or just right. Either you got the answer or you know which possible answer to check next. Took me a total of under 10 seconds.
Nobody cares that you figured out the answer in "under 10 seconds" because it's a very simple problem and, more importantly, the goal is not getting the result but rather to provide some instruction in building and solving Algebraic equations. But it's so cool that you got the answer. Good job.
The actual answer d) 10 did not show on my screen till the very end of the video but I used the deductive method also. This was a good refresher though. The instructor did state the answer at the beginning.
This problem requires two variables, Ann and Dan, to express the age relationships. Initially it is given that: 1. Dan (D) is six years older than Ann (A). 2. In two years Dan will be twice as old as Ann. 1. D = A + 6 present age 2. D = 2A + 2 future age Rearrange formulas such as now A is the dependent variable. 1. A = D - 6 present age 2. A = (D - 2)/2 future age Now combine the two equations to find the age of Dan D - 6 = (D - 2)/2 multiply both sides by two to eliminate the fraction 2 * (D - 6) = D - 2 multiply the left side by 2 2D - 12 = D - 2 add 12 to both sides 2D = D + 10 subtract D from both side to get the final answer. D = 10
Yes, that is essentially the way I approached it. Except I went: Let d be Dan's present age. Let a be Ann's present age. 1) d - 6 = a 2) d + 2 = 2a Substituting expression for a from equation 1) into equation 2) gives: d + 2 = 2(d - 6) = d + 2 = 2d - 12 = - d + 2 = - 12 = - d = - 10 = d = 10. I did get stuck initially as I wanted to add 2 years to Ann's age as well. Thus for equation 2) d + 2 = 2a + 2. But this yields the wrong answer. Then I realised that d is the dependent variable (I think?), and the two years have already been added on the left-hand side. In other words, in two year's time Dan's age is simply twice Ann's age. No need for adding the 2 to the right-hand side.
I started at Ann being 0 and Dan being 6 and added 2 to each figure and came to 2 and 8. Thereafter i continously added 1 to both 2 and 8 until i reached 6 and 12 and worked. 2 years back and came to 4 and 10. Done mentally. No pen, paper or equations necessary. Done under a minute
Just use the answers they are there to limit choices and save time. Wast of time plugging in unknown variables when there are 4 known variables. Took 10 seconds honestly.
I did it differently. Dan is 6 years older, so when Ann is 6 and he is 12, then he is twice as old as Ann,so 6x2.. but he won't be twice as old in 2 years, so 6x2-2
I am a Grandparent and have told my children to view your TH-cam for help with their children's Math problems! P.S. The green chalkboard brings back great memories of K-12!!
Love the two variable, two equation word problems... unknowns: Ages: Dan : D Ann : A equations: D = A + 6 eq.1 D + 2 = 2×(A + 2) eq.2 D = -2 +2A + 4 D = 2A + 2 eq 2.1 collect formulas D = A + 6 eq.1 D = 2A + 2 eq.2.1 subtract eq 2.1 from eq.1 0 = -A + 4 A = 4 sol.1 continue D = A + 6 eq.1 A = 4 D = 4 + 6 D = 10 sol.2 Collect solutions A = 4 sol.1 D = 10 sol.2 VERIFY D =? A + 6 eq.1 D =? 2A + 2 eq 2.1 with A = 4 sol.1 D = 10 sol.2 D =? A + 6 eq.1 10 =? 4 + 6 10 =❤ 10✔️ D =? 2A + 2 eq 2.1 10 =? 2(4) + 2 10 =? 8 + 2 10 =❤ 10✔️
Let D = Dan; Let A-= Ann; D-6=A; ergo: D=A+6; D+2=2(A+2) substitute A+6 for D and we get A+6+2=2(A+2); simplify: A+8 = 2A+4; Subtract A from both sides and we get 8=A+4; 4=A, ergo D=10 The answer is D.
Today you don't need to be great in math if you are planning to take engineering all you need to do is open you tube.every problem lesson is all there. Thank you sir. Algebra, trigonometry geometry were my favorites during college.because I am poor in English😄😄😄🇵🇭🇵🇭🇵🇭
I never understood algebra when I was young.I found it to be tricky math that was like unfair. But I found that sometimes common sense can work really well with algebra instead of all that scribbling. So looking at the equation, I said okay well. Dan being 6 years older and he's gonna be twice as old as Anne in 2 years. I like figure okay. Well, 12 is the only number that Dan could be in 2 years Which would make Ann 4 now and Dan 10 now. In 2 years Ann will be 6 and Dan will be 12. Common sense. I did this easily in my head without all that confusion. Algebra make sense to me now but I still think is a stupid way to solve a problems with the scribbling. Takes more common sense and intuation to solve the missing piece of information that is mysteriously hidden behind X Y or Z. The teachers never explained it right so I could never learn it in school. I learned it in my late 20's. But I learned common sense way before then. Ha ha never knew I was executing algebra to survive. Cause life is full of mysterious information lying behind X Y and Z. Figure it out and you've solved a mystery.
A problem I had in school was that I could never show my work as I always, as I did here, solve the problem in my head to get the right answer in about 15 seconds. I would then test out my answer by doing basic math with no intervening steps shown as it was done intuitively in my head.
I had the same issue but my teacher said I either did it her way or a failing grade was on the horizon. I never did it her way but i almost always had the correct answer- it was odd
I didn't even use the maths per say... I just figured it out by process of illimitation based on the answer choices vs whether that worked logically with the sentence and came up with the answer of 10. I'm glad I was right.
😊😊😊. That works if it’s multiple choice. It’s been over 50 years since high school math but I don’t remember ever having a word problem with multiple choice options.
Was sooooo confused in junior high school and I'm somewhat in your age group(I think) and I'm still unbelievably crazy in my mind. I got an ulcer over algebra and I was transferred to bookkeeping and guess what? I became an accountant and I still don't know algebra. Hope you can change that. I'm not giving up and I've got plenty of Maalox....lol.😂
Greetings. Dan is presently 10 years old. These were my absolute favourite problems in studying algebra. Now for the solution. We will start by assigning the value X to represent Ann's age. Now, when Ann is X years old, Dan will be (X+6) since he is 6 years older. Moving forward, in 2 years time, Ann and Dan will all be 2 years older. That is Dan's age will (X+6+2) years, and Ann's age will be (X+2). Using the information that after 2 years are added to their initial ages Dan's age will be twice Ann's age, we have (X+6+2)=2(X+2). Solving for X gives X=4. Therefore, Dan's current age is (4+6) years, equals 10 years old. When Dan was 10, Ann was 4 and in 2 years, Dan would have become 12 while Ann would have become 6 making Dan twice as old as Ann after 2 years.
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Simultaneous equations! D = A + 6 {First Equation} D + 2 = 2(A+2) = 2A + 4 D = 2A + 4 - 2 = 2A + 2 D = 2A + 2 {-D=-2A-2 Second Eq.} -_____________ {subtract 2nd from 1st} 0 = -A + 4 A = 4 Ann is 4, and Dan is 4+ 6 = 10 (ANSWER) (At the risk of being obvious, the most important equation is: D+2=2(A+2) "In 2 years from now, Dan's age will be TWICE Ann's age, when she is also 2 years older, too.") ...Notice that all variables always represent present time, and 2 years in the future is X+2. SIMULTANEOUS EQUATIONS is an extremely useful skill set with numerous practical applications!!
The method described in your video invites mistakes because the principal equation, (x+8)=2(x+2), DOES NOT RELATE LITERALLY TO THE PROBLEM! Therefore the student is entirely unable to DOUBLE CHECK his progress before generating a solution. It's always best to have a working equation that can be word for word verified with the original problem, to weed out errors. We cannot say "X plus 8 equals twice X plus 2" and find those words in the word problem, since X and 8 are nowhere to be found. While using x for Ann's age makes the arithmetic easier, students are likely prone to forget that x is not the variable representing the answer, and this will often induce errors when trying to juggle all these concepts at once. Simultaneous equations allows you to go word-for-word through the problem and back check accuracy, eliminating most common mistakes, and making the solution ENJOYABLE!!
Finding Dan original age easier in my Steps of elimination: Ann =x In 2yrs Time x+6+2=2(x+2) x+8=2x+4 x+(8-4)=2x x+4=2x x=2x-4 (x-2x)=-4 -x= -4 OR x=4 because (2-minus) = plus So Ann is originally 4 Dan is originally 4+6 = 10 PROOF 4+6+2= 2(4+2) 12 = 8+4 12 = 12 The Instructor tries to explain procedures but too many words are confusing . Signed 🇯🇲
@@brownr749 Well the question was.. how old is he NOW not how old would he be in two years. The answer has to be He is ten, (now) and Anne is 4 now. then he is12 in two years time, and Anne is 6 in two years time. Thus he is twice her age then.
@@ebonypegasus9864 I was wrong...If Dan is 10 now…. in two yrs he will be 12 And in the those two years in the future, Ann’s age would be 6…two years ago she was 4 When Ann was 4 and Dan 6years older .. that would make him 10 now. Dan is now 10 in two years he will be 12, and Ann will be 6….meaning Dan would be twice Ann’s age… she being 6. A heck of a mind twister!
Let dans age = d and let anns age = a, therefore d=a+6..... equation i and also d=2a+2 in two years time...... equation ii Now subtract ii from i We have d-d=a+6-(2a+2) 0=a+6-2a-2 Or a=4= anns age Substitute a in equation i d=4+6. d=10=dans age Therefore answer is d......QED
Actually, if Ann is now 4 and Dan is now 10, he is now 'more' than twice as old as Ann. He doesn't become exactly twice as old as Ann until Ann is 6 and Dan is 12. So, the answer is Dan is twice as old as Ann when Dan is 12.
I was wrong...If Dan is 10 now…. in two yrs he will be 12 And in the those two years in the future, Ann’s age would be 6…two years ago she was 4 When Ann was 4 and Dan 6years older .. that would make him 10 now. Dan is now 10 in two years he will be 12, and Ann will be 6….meaning Dan would be twice Ann’s age… she being 6. A heck of a mind twister!
Figured out an algebraic equation 2(A+2)=(A+2) + 6 Ann = 4 Dan = 10
2 หลายเดือนก่อน
solve for Ann's age first: dan 6 yrs older than ann ; then in 2 yrs he will be twice as old. If you take 6yrs now and subtract 2yrs then x=4 for Ann's age; because Dan will be twice as old in 2 years: first solve 4+6=10 Dan's age now, next take Ann's age 4 add 2yrs =6, then add 2+10= 12 for Dan's age: take Dan's age and divide with Ann's age (12/6 =2)
This seemed a complicated approach to me. Wouldn't it be simpler ttook do it this way: Dan is 6 years older than Ann, therefore he was 6 when Ann was born. This means Ann would have to 6 for Dan to be twice her age making him 12 At that time. As this won't happen for another 2 years, Dan is currently 12 years - 2 years, so Dan is 10
@@ellentronicmistress4969the purpose of maths is to come to a solution; not to make it so complicated as to make people scared of it and think it is out of their reach. Make others think it is achievable at least.
@@elisefoad2326 Maths teaching today is as much aboutwhy things work. and not just how to make them work. It's not just about teaching short-cuts and actually the opposite to your assertion is true in my opinion, because teaching children properly helps them to understand the subject more and thus they enjoy it more.
If Dan is now 14 and Ann is 8. (D = A +6). So then in 2 years Dan will be 16 which is twice as old as Ann is now. The question is badly worded as it doesn't say "Twice as old as Ann will be in 2 years".
Someone commented on a previous problem and made a snarky comment which made me laugh. I am 75 and you can teach old dogs new tricks. I decided to see if I followed this site could I refresh or learn math skills. I was terrible in math and struggled all my life. I am not going to deal with algebra too much or geometry but I have made some improvements on the simple basic stuff just by doing these problems. Now it is fun to challenge myself because I don’t have Sister Mary Joseph standing over me sternly chastising me. Lol
D = A + 6 ---> A = D - 6 In 2 years D + 2 = 2 (A + 2) D + 2 = 2A + 4 D = 2A + 2, and A = D - 6, thus D = 2(D - 6) + 2 = 2D - 12 + 2 D = 2D - 10 10 = 2D - D 10 = D
Dan is 6 years older than Ann ... so their ages are X and X + 6 In two tears he will be twice as ald ... X + 6 + 2 = 2 (X + 2) X + 8 = 2X + 4 8 - 4 = 2X - 2 4 = X Ann is 4 Dan is 10 and in two years they will be 6 and 12
Mmm, looks like algebra to me... I can see 4 equations: (1) D1 = A1 + 6 (D1 is the one we are looking for !) (2) D2 = D1 + 2 = (A1+6) + 2 = A1 + 8 so A1 = D2 - 8 (3) A2 = A1 + 2 so A2 = (D2-8) + 2 = D2 - 6 (4) D2 = A2 x 2 so D2 = (D2-6) . 2 so D2 = 2D2 - 12 and D2 = 12 yo D1 = D2 - 2 so D1 = 10 yo so the answer is D... I like algebra !
I can solve it in less than 1 min using the model method. In Singapore, we used the model method. This is a 10 year old (primary 4 school student 😎type of question)
In school... You want kids to pay attention to this stuff? Substitute Anne with a Temporal Flux Modulator and Dan with Flux capacitor. Due to a faulty mount holdijng down the flux capacitor, it didn't move in sync with the entire Delorean so now the flux capacitor is 6 years older than the temporal flux modulator and thus incompatible. All we know is that in two years, the the Flux capacitor will have existed exactly twice that of the temporal flux modulator. We need to find the how many years of decay the flux capacitor has undergone to return to the present.
At the title card, my answer is d) 10. If Dan is 10 now, then Ann is 4. Add 2 years, and Dan is 12, with Ann being 6. None of the other options work out.
Dan is 6 yrs older than Ann; D=A+6; In two years; (D+2); (A+2); Dan will be twin as old as Ann; D+2=2(A+2); Since D=A+6; therefore (A+6)+2=2A+4 ; A+8=2A+4; 8=A+4; eliminate the A's form both sides; How old is Dan now? 4=A; Since Dan is 6 yrs older than Ann right now; Dan is 10!
Easy to work out by process of elimination, eg if he was 12 now she would be 6, in two years he would be 14 but Ann would only be 6, work through each possible answer like this, obviously only one work.
I got 10 but I had to think hard about it and first I wanted to put it in an equation but I forgot my math at 74... ha, ha.... I did not do too much math since high school. I got to the point of x = x + 6.... I did not write anything down, I've just got up; and then I said what about Ann is 1 or 2 or 3...etc. and I when I got to 2 it made sense the answer was 10.
As a maths tutor, all I can say is, I am very happy that I don't teach mathematics like this. There is a fault in the question asked. Maybe it's a difference between American and British way of expression.
I think some of you are missing the point. He is teaching us how to solve a simple word problem using algebra so that when you have a more difficult problem, you know how to solve it.
The problem with presenting a comparatively convoluted algebraic solution when there is a much simpler logical solution, is that it creates the impression (or even worse, reinforces a pre-existing impression) that algebra is complicated and pointless and only exists so that mathematicians can make themselves feel clever, and make other people feel stupid. At the very least, showing the algebraic solution should come with a loud and prominent, up-front health warning: "you do not need this tool to answer this question - I am just using this question as a way to introduce a tool that will be useful elsewhere". But a much better way to introduce algebra would be for the teacher to devise a problem where some simple algebra is the natural and obvious solution, not a silly contrivance like this.
So the comment that people leave with the math situation they don’t realize how many people is out there have issues with mathematics and I am one of them
Easy enough to figure out in your head. In 2 years Dan will still be 6 years older than Ann. If he is twice as old as Ann at that point, then Dan has to be 12 and Ann has to be 6. Back up 2 years to get the current ages.
I got the right answer by reading and thinking. But knowing i failed because I don’t have the problem written out. By watching your way didn’t help me cause that’s not the way i thought out the problem. And I couldn’t figure out how to write out what was in my head. Crap.
Maybe I'm wrong. I'm baffled over this. 10? He is twice her age? Then, that makes her 5. Part of the premise is he is 6 years older. Being 6 years older than someone's DOB can never change. So, how is she 5 and he's 10? That's only 5 years older....can't make sense out of this.
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This teacher takes his time and explains each step very clearly. So, stop saying he talks too much and to hurry up. No, if you're bored with his teaching, just move on and leave his page.
We're not saying he talks too much. We are saying that the seeming tangents he sometimes goes off on are both distracting and not germain to the solution. In spite of this, I enjoy his explanations.
This is one of the best Maths teacher but I need to buy time to sit down and watch his videos.
You really don’t need to take so long, no one has that much time or patience.
I love watching your videos to relax. The old saying, "Use it or loose it," really does apply to Math.
His answer is wrong. The correct answer is 12.
@brownr749 , the answer is 10. In two years, he will be 12, twice Ann's age.
@@1975KyleDavid My math is different than yours. In the premise, Dan is 6 years older than Ann. ….if he’s 10 and suppose to be twice her age, that means Ann is 5. Can’t be… when he suppose to be twice her age...and 6 years older. Her 5 and he’s 10 doesn’t add up to 6 years older.
@@1975KyleDavid Can you at least explain how you came up with your answer? I explained mine in detail. You cannot do the same?
@@1975KyleDavid I was wrong...and do the explaining for you...If Dan is 10 now…. in two yrs he will be 12
And in the those two years in the future, Ann’s age would be 6…two years ago she was 4
When Ann was 4 and Dan 6years older .. that would make him 10 now.
Dan is now 10 in two years he will be 12, and Ann will be 6….meaning Dan would be
twice Ann’s age… she being 6. A heck of a mind twister!
one of the best math teachers on utube is " the organic chem tutor"..........clear and succinct
He's confusing as heck...and he comes up with the wrong answer...the correct answer is 12.
I agree that he talks & talks & talks to teach you need to simplify the process.
Exactly!
I love your videos. You explain math in very easy terms! I was in honors math in high school but forgot a lot of it in the last 50 years, but you make it easy to bring it all back.
No need for any equations. Start from the possible answers. Pick any one. It takes just a moment to see if it is too high, too low, or just right. Either you got the answer or you know which possible answer to check next. Took me a total of under 10 seconds.
Having the 4 possible answers makes it easy as you can work back, but it takes a bit of thinking to actually work it out.
Nobody cares that you figured out the answer in "under 10 seconds" because it's a very simple problem and, more importantly, the goal is not getting the result but rather to provide some instruction in building and solving Algebraic equations. But it's so cool that you got the answer. Good job.
I used the same process but it took me a good minute
The actual answer d) 10 did not show on my screen till the very end of the video but I used the deductive method also. This was a good refresher though. The instructor did state the answer at the beginning.
Plug in
This problem requires two variables, Ann and Dan, to express the age relationships.
Initially it is given that: 1. Dan (D) is six years older than Ann (A). 2. In two years Dan will be twice as old as Ann.
1. D = A + 6 present age
2. D = 2A + 2 future age
Rearrange formulas such as now A is the dependent variable.
1. A = D - 6 present age
2. A = (D - 2)/2 future age
Now combine the two equations to find the age of Dan
D - 6 = (D - 2)/2 multiply both sides by two to eliminate the fraction
2 * (D - 6) = D - 2 multiply the left side by 2
2D - 12 = D - 2 add 12 to both sides
2D = D + 10 subtract D from both side to get the final answer.
D = 10
nice
Now that I can follow 👍
Easier
D=2A+2
D=A+6
Subtract
0=A-4
A=4, D=6
Yes, that is essentially the way I approached it. Except I went:
Let d be Dan's present age. Let a be Ann's present age.
1) d - 6 = a
2) d + 2 = 2a
Substituting expression for a from equation 1) into equation 2) gives:
d + 2 = 2(d - 6)
= d + 2 = 2d - 12
= - d + 2 = - 12
= - d = - 10
= d = 10.
I did get stuck initially as I wanted to add 2 years to Ann's age as well. Thus for equation 2) d + 2 = 2a + 2. But this yields the wrong answer. Then I realised that d is the dependent variable (I think?), and the two years have already been added on the left-hand side. In other words, in two year's time Dan's age is simply twice Ann's age. No need for adding the 2 to the right-hand side.
You only need to use one variable as is shown in the video. It's a much cleaner way to solve problems such as this.
I started at Ann being 0 and Dan being 6 and added 2 to each figure and came to 2 and 8. Thereafter i continously added 1 to both 2 and 8 until i reached 6 and 12 and worked. 2 years back and came to 4 and 10. Done mentally. No pen, paper or equations necessary. Done under a minute
Just use the answers they are there to limit choices and save time. Wast of time plugging in unknown variables when there are 4 known variables. Took 10 seconds honestly.
Me too
I did it differently.
Dan is 6 years older, so when Ann is 6 and he is 12, then he is twice as old as Ann,so 6x2.. but he won't be twice as old in 2 years, so 6x2-2
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That's great and it works
I am a Grandparent and have told my children to view your TH-cam for help with their children's Math problems! P.S. The green chalkboard brings back great memories of K-12!!
Love the two variable, two equation word problems...
unknowns:
Ages:
Dan : D
Ann : A
equations:
D = A + 6 eq.1
D + 2 = 2×(A + 2) eq.2
D = -2 +2A + 4
D = 2A + 2 eq 2.1
collect formulas
D = A + 6 eq.1
D = 2A + 2 eq.2.1
subtract eq 2.1 from eq.1
0 = -A + 4
A = 4 sol.1
continue
D = A + 6 eq.1
A = 4
D = 4 + 6
D = 10 sol.2
Collect solutions
A = 4 sol.1
D = 10 sol.2
VERIFY
D =? A + 6 eq.1
D =? 2A + 2 eq 2.1
with
A = 4 sol.1
D = 10 sol.2
D =? A + 6 eq.1
10 =? 4 + 6
10 =❤ 10✔️
D =? 2A + 2 eq 2.1
10 =? 2(4) + 2
10 =? 8 + 2
10 =❤ 10✔️
Let D = Dan; Let A-= Ann; D-6=A; ergo: D=A+6; D+2=2(A+2) substitute A+6 for D and we get A+6+2=2(A+2); simplify: A+8 = 2A+4; Subtract A from both sides and we get 8=A+4; 4=A, ergo D=10 The answer is D.
x = Ann's current age & x+6 = Dan's current age. x+2 = (x+8)/2 → 2x+4 = x+8 → x+4 = 8 → x = 4 , Therefore x+6 = 4+6 = 10. QED
Overkill!
Lovely! :)
Dan is ten years old. I got it correct pretty quickly! I generally hate word problems, but this one was easy!
Today you don't need to be great in math if you are planning to take engineering all you need to do is open you tube.every problem lesson is all there. Thank you sir. Algebra, trigonometry geometry were my favorites during college.because I am poor in English😄😄😄🇵🇭🇵🇭🇵🇭
Reading comments..SO MANY OF U make this sound so hard.. NOW think of the age range this is meant for..NOW give ur results..!!!
I never understood algebra when I was young.I found it to be tricky math that was like unfair.
But I found that sometimes common sense can work really well with algebra instead of all that scribbling.
So looking at the equation, I said okay well. Dan being 6 years older and he's gonna be twice as old as Anne in 2 years. I like figure okay. Well, 12 is the only number that Dan could be in 2 years Which would make Ann 4 now and Dan 10 now. In 2 years Ann will be 6 and Dan will be 12. Common sense.
I did this easily in my head without all that confusion. Algebra make sense to me now but I still think is a stupid way to solve a problems with the scribbling. Takes more common sense and intuation to solve the missing piece of information that is mysteriously hidden behind X Y or Z.
The teachers never explained it right so I could never learn it in school. I learned it in my late 20's. But I learned common sense way before then. Ha ha never knew I was executing algebra to survive. Cause life is full of mysterious information lying behind X Y and Z. Figure it out and you've solved a mystery.
A problem I had in school was that I could never show my work as I always, as I did here, solve the problem in my head to get the right answer in about 15 seconds. I would then test out my answer by doing basic math with no intervening steps shown as it was done intuitively in my head.
I had the same issue but my teacher said I either did it her way or a failing grade was on the horizon. I never did it her way but i almost always had the correct answer- it was odd
I didn't even use the maths per say... I just figured it out by process of illimitation based on the answer choices vs whether that worked logically with the sentence and came up with the answer of 10. I'm glad I was right.
😊😊😊. That works if it’s multiple choice. It’s been over 50 years since high school math but I don’t remember ever having a word problem with multiple choice options.
Was sooooo confused in junior high school and I'm somewhat in your age group(I think) and I'm still unbelievably crazy in my mind. I got an ulcer over algebra and I was transferred to bookkeeping and guess what? I became an accountant and I still don't know algebra. Hope you can change that. I'm not giving up and I've got plenty of Maalox....lol.😂
Greetings. Dan is presently 10 years old. These were my absolute favourite problems in studying algebra. Now for the solution. We will start by assigning the value X to represent Ann's age. Now, when Ann is X years old, Dan will be (X+6) since he is 6 years older. Moving forward, in 2 years time, Ann and Dan will all be 2 years older. That is Dan's age will (X+6+2) years, and Ann's age will be (X+2). Using the information that after 2 years are added to their initial ages Dan's age will be twice Ann's age, we have
(X+6+2)=2(X+2). Solving for X gives
X=4. Therefore, Dan's current age is
(4+6) years, equals 10 years old.
When Dan was 10, Ann was 4 and in 2 years, Dan would have become 12 while Ann would have become 6 making Dan twice as old as Ann after 2 years.
MINI
DISSERTATION
MASTERPIECE 🏆
▪️INTRODUCTION 💯
▪️VALIDATION 💯
▪️CALCULATIONS 💯
▪️CONCLUSIONS 💯
👌🏾……. Purity in analysis
and rationale ❗️
We can use you in
Washington Senator❗️
Got it! Because I worked out how each of the multiple choice answers worked out.
😂
I'd use A and D for variable letters
How about if you multiply the 6 by 2 n subtract the 2 years to find current age of Dan =10?
Simultaneous equations!
D = A + 6 {First Equation}
D + 2 = 2(A+2) = 2A + 4
D = 2A + 4 - 2 = 2A + 2
D = 2A + 2 {-D=-2A-2 Second Eq.}
-_____________ {subtract 2nd from 1st}
0 = -A + 4
A = 4
Ann is 4, and Dan is 4+ 6 = 10 (ANSWER)
(At the risk of being obvious, the most important equation is: D+2=2(A+2) "In 2 years from now, Dan's age will be TWICE Ann's age, when she is also 2 years older, too.")
...Notice that all variables always represent present time, and 2 years in the future is X+2.
SIMULTANEOUS EQUATIONS is an extremely useful skill set with numerous practical applications!!
The method described in your video invites mistakes because the principal equation, (x+8)=2(x+2), DOES NOT RELATE LITERALLY TO THE PROBLEM! Therefore the student is entirely unable to DOUBLE CHECK his progress before generating a solution. It's always best to have a working equation that can be word for word verified with the original problem, to weed out errors. We cannot say "X plus 8 equals twice X plus 2" and find those words in the word problem, since X and 8 are nowhere to be found. While using x for Ann's age makes the arithmetic easier, students are likely prone to forget that x is not the variable representing the answer, and this will often induce errors when trying to juggle all these concepts at once. Simultaneous equations allows you to go word-for-word through the problem and back check accuracy, eliminating most common mistakes, and making the solution ENJOYABLE!!
6 to be twice her age is at least 12 -2 years means he is 10 now with logical reasoning without all the math gymnastics. 🤣🤣🤣🤣
I’m with ya %100 !! And that’s my math !! 🤣🤣
I used 2 EquationsD for Dan A for Ann D=A+6 and D+2=2A.Substitute 2A-2 =D Solve 2A-2=A+6 A=4 Dan = 4+6 =10
Wrong. From 2A-2=A+6 you will get A=8 and not A=4
Finding Dan original age easier in my Steps of elimination: Ann =x
In 2yrs Time
x+6+2=2(x+2)
x+8=2x+4
x+(8-4)=2x
x+4=2x
x=2x-4
(x-2x)=-4
-x= -4 OR x=4 because (2-minus) = plus
So Ann is originally 4
Dan is originally 4+6 = 10
PROOF
4+6+2= 2(4+2)
12 = 8+4
12 = 12
The Instructor tries to explain procedures but too many words are confusing .
Signed 🇯🇲
I think Dan should be 10 now and Ann is 4…
yes in two years she'll be 6 and he'll be 12 which makes him half as old.
@@DeeDee-mv2uw😢😮Ý
...the answer is actually 12...no matter how you look at it, the answer will never be 10.
@@brownr749 Well the question was.. how old is he NOW not how old would he be in two years. The answer has to be He is ten, (now) and Anne is 4 now. then he is12 in two years time, and Anne is 6 in two years time. Thus he is twice her age then.
@@ebonypegasus9864 I was wrong...If Dan is 10 now…. in two yrs he will be 12
And in the those two years in the future, Ann’s age would be 6…two years ago she was 4
When Ann was 4 and Dan 6years older .. that would make him 10 now.
Dan is now 10 in two years he will be 12, and Ann will be 6….meaning Dan would be
twice Ann’s age… she being 6. A heck of a mind twister!
Wow! Distributive Property. I haven't heard that term in over 35 years! I'm going to "relearn" math!
I am so glad that I came across your channel! You have a new subscriber!
💛💛💛💛💛💛💛
Enjoy your channel. At my age I have forgotten a lot of math computations so like that you go over details.
Now, let Ann' age is x, thus Dan's age is x+6.
Next 2 yrs, Ann age is x+2 and Dan age (x+6)+2.
And Dan age is twice of Ann
2(x+2)=(x+6)+2
x=4.
Let dans age = d and let anns age = a,
therefore d=a+6..... equation i
and also d=2a+2 in two years time...... equation ii
Now subtract ii from i
We have d-d=a+6-(2a+2)
0=a+6-2a-2
Or a=4= anns age
Substitute a in equation i
d=4+6.
d=10=dans age
Therefore answer is d......QED
Actually, if Ann is now 4 and Dan is now 10, he is now 'more' than twice as old as Ann. He doesn't become exactly twice as old as Ann until Ann is 6 and Dan is 12. So, the answer is Dan is twice as old as Ann when Dan is 12.
Or, until Dan is 12 and Ann is 6, he will be 'more' than twice as old as Ann.😊.
It is a badly compiled question as it should state Dan would be twice as old as Ann is now. Confusing.
@@ians.339 ...confusing? I don't see how anyone can get the answer being 10, no matter how you arrange his statements.
I was wrong...If Dan is 10 now…. in two yrs he will be 12
And in the those two years in the future, Ann’s age would be 6…two years ago she was 4
When Ann was 4 and Dan 6years older .. that would make him 10 now.
Dan is now 10 in two years he will be 12, and Ann will be 6….meaning Dan would be
twice Ann’s age… she being 6. A heck of a mind twister!
Figured out an algebraic equation
2(A+2)=(A+2) + 6
Ann = 4
Dan = 10
solve for Ann's age first: dan 6 yrs older than ann ; then in 2 yrs he will be twice as old. If you take 6yrs now and subtract 2yrs then x=4 for Ann's age; because Dan will be twice as old in 2 years: first solve 4+6=10 Dan's age now, next take Ann's age 4 add 2yrs =6, then add 2+10= 12 for Dan's age: take Dan's age and divide with Ann's age (12/6 =2)
Dan is 6 years old now and Ann is 2.
Good instructor overall👍
This seemed a complicated approach to me. Wouldn't it be simpler ttook do it this way:
Dan is 6 years older than Ann, therefore he was 6 when Ann was born.
This means Ann would have to 6 for Dan to be twice her age making him 12 At that time.
As this won't happen for another 2 years, Dan is currently 12 years - 2 years, so Dan is 10
Your reasoning is correct but the point is learning how to use algebra to solve problems like this
@@ellentronicmistress4969the purpose of maths is to come to a solution; not to make it so complicated as to make people scared of it and think it is out of their reach. Make others think it is achievable at least.
@@elisefoad2326 Maths teaching today is as much aboutwhy things work. and not just how to make them work. It's not just about teaching short-cuts and actually the opposite to your assertion is true in my opinion, because teaching children properly helps them to understand the subject more and thus they enjoy it more.
If Dan is now 14 and Ann is 8. (D = A +6). So then in 2 years Dan will be 16 which is twice as old as Ann is now. The question is badly worded as it doesn't say "Twice as old as Ann will be in 2 years".
Someone commented on a previous problem and made a snarky comment which made me laugh. I am 75 and you can teach old dogs new tricks. I decided to see if I followed this site could I refresh or learn math skills. I was terrible in math and struggled all my life. I am not going to deal with algebra too much or geometry but I have made some improvements on the simple basic stuff just by doing these problems. Now it is fun to challenge myself because I don’t have Sister Mary Joseph standing over me sternly chastising me. Lol
He leaves no room for doubt.
D = A + 6 ---> A = D - 6
In 2 years
D + 2 = 2 (A + 2)
D + 2 = 2A + 4
D = 2A + 2, and A = D - 6, thus
D = 2(D - 6) + 2
= 2D - 12 + 2
D = 2D - 10
10 = 2D - D
10 = D
Dan is 10 . X+6 is Dan ann is x. In two yrs Dan is x+6+2 and Ann will be x+2. Equation is x+6+2=2(x+2) and solve. X is 4
Dan is 6 years older than Ann ... so their ages are X and X + 6
In two tears he will be twice as ald ... X + 6 + 2 = 2 (X + 2)
X + 8 = 2X + 4
8 - 4 = 2X - 2
4 = X
Ann is 4 Dan is 10 and in two years they will be 6 and 12
Mmm, looks like algebra to me... I can see 4 equations:
(1) D1 = A1 + 6 (D1 is the one we are looking for !)
(2) D2 = D1 + 2 = (A1+6) + 2 = A1 + 8 so A1 = D2 - 8
(3) A2 = A1 + 2 so A2 = (D2-8) + 2 = D2 - 6
(4) D2 = A2 x 2 so D2 = (D2-6) . 2 so D2 = 2D2 - 12 and D2 = 12 yo
D1 = D2 - 2 so D1 = 10 yo so the answer is D...
I like algebra !
I wish you'd get to the point fast. You drag things out for far too long.😩The expression is 6+x+2=2(x+2) solve for x.
I can solve it in less than 1 min using the model method. In Singapore, we used the model method. This is a 10 year old (primary 4 school student 😎type of question)
In school... You want kids to pay attention to this stuff? Substitute Anne with a Temporal Flux Modulator and Dan with Flux capacitor. Due to a faulty mount holdijng down the flux capacitor, it didn't move in sync with the entire Delorean so now the flux capacitor is 6 years older than the temporal flux modulator and thus incompatible. All we know is that in two years, the the Flux capacitor will have existed exactly twice that of the temporal flux modulator. We need to find the how many years of decay the flux capacitor has undergone to return to the present.
You added a long drawn out solution to a problem most people can solve in their head in seconds
He showed the correct way to solve it using algebra. Many people are just starting their algebra journey and these videos are for them.
And for the sake of those who could not solve it in seconds, John, graciously explain step by step. So thank you John!!
I apologize I miss spoke
At the title card, my answer is d) 10.
If Dan is 10 now, then Ann is 4. Add 2 years, and Dan is 12, with Ann being 6.
None of the other options work out.
His is twice 6 in two years.
Equation. DAN
6x2=X+2
12 = X+2
DAN =10
ANN = 10-6
20 minutes video is unrealistic for something like that, surely a good explanation could still be given in a shorter time.
Dan is 6 yrs older than Ann; D=A+6;
In two years; (D+2); (A+2);
Dan will be twin as old as Ann; D+2=2(A+2);
Since D=A+6; therefore (A+6)+2=2A+4 ;
A+8=2A+4;
8=A+4; eliminate the A's form both sides;
How old is Dan now? 4=A; Since Dan is 6 yrs older than Ann right now; Dan is 10!
I did this and got the answer (×+6)+(x-6)=2(×2+2) raise to power 2
×=2(×+2)raise to power 2
=8+2 years =10years
Easy to work out by process of elimination, eg if he was 12 now she would be 6, in two years he would be 14 but Ann would only be 6, work through each possible answer like this, obviously only one work.
Answer:@1:53
got it.... calculate or substitute using answer options thanks for the fun.
When would you use this in every day life. Only in school math class.
Dan is 10yrs now and Ann is 4. In two years he will be twice the age of Ann which is 12 and Ann will be 6.
This is the first one i got right. he gave us 4 'answers', process of elimination.
√8 2^3 (x+2x-3)
Practice = Skill
10. I just plugged in all the answers. 10 is the only option that works.
Even if it is a leap year you woulde just added one +2 =equals three =nine years old
Ask Dan his age.
D=A+6, D=2A-2 2A-2=A+6 A=4, D=4+6=10 Why must we make things complicated?
D=2A - 2 is incorrect
should be
D + 2 = 2(A + 2)
D = 2(A+2) - 2
D = 2A + 2
10 years old now
Why use X
Why not use "D" for Dan's current age and "A" for Ann's current age.
Mainly for those beginning algebra
D. Final answer.
I got 10 but I had to think hard about it and first I wanted to put it in an equation but I forgot my math at 74... ha, ha.... I did not do too much math since high school. I got to the point of x = x + 6.... I did not write anything down, I've just got up; and then I said what about Ann is 1 or 2 or 3...etc. and I when I got to 2 it made sense the answer was 10.
As a maths tutor, all I can say is, I am very happy that I don't teach mathematics like this. There is a fault in the question asked. Maybe it's a difference between American and British way of expression.
d) 10 years old . In two years he will be 12 and she will be 6
Not watching the video or reading the comments. 6+2=2x ---- 4 = x ---- 4+6=10 ---- 10+2 = 12 Dan is 10 and Ann is 4.
Twice as old it would be 12 but 2 years older than 10
I think some of you are missing the point. He is teaching us how to solve a simple word problem using algebra so that when you have a more difficult problem, you know how to solve it.
The problem with presenting a comparatively convoluted algebraic solution when there is a much simpler logical solution, is that it creates the impression (or even worse, reinforces a pre-existing impression) that algebra is complicated and pointless and only exists so that mathematicians can make themselves feel clever, and make other people feel stupid.
At the very least, showing the algebraic solution should come with a loud and prominent, up-front health warning: "you do not need this tool to answer this question - I am just using this question as a way to introduce a tool that will be useful elsewhere".
But a much better way to introduce algebra would be for the teacher to devise a problem where some simple algebra is the natural and obvious solution, not a silly contrivance like this.
The answer is 10. Because she is 4. Inb2 years Ann will be 6 and Dan will be 12.
D 10. I just could see in my head the correct answer without doing an equation.
Dan is 10 years old while Ann is 4, in two years Dan will be 12 while Ann will be 6. That makes Dan double Ann's age
I’ve never been good at word problems.
So the comment that people leave with the math situation they don’t realize how many people is out there have issues with mathematics and I am one of them
took me seconds: Dan is 10 years old
Easy enough to figure out in your head. In 2 years Dan will still be 6 years older than Ann. If he is twice as old as Ann at that point, then Dan has to be 12 and Ann has to be 6. Back up 2 years to get the current ages.
I got the right answer by reading and thinking. But knowing i failed because I don’t have the problem written out. By watching your way didn’t help me cause that’s not the way i thought out the problem. And I couldn’t figure out how to write out what was in my head. Crap.
Dan 10 yrs, Ann 4yrs.
😂😂😂😂😂 he does talk sooooo much I hope he has real friends
let his age be A
(A + 2) ÷ 2 = 6
A + 2 = 12
A = 10
I figured how to do it at 5:46
Dan is 10!
15:31 in the video?
Ooops.
Dan is still 6 years old now
A more interesting question might be, How old will Dan be when he figures out how to solve this problem?
Maybe I'm wrong. I'm baffled over this. 10? He is twice her age? Then, that makes her 5. Part of the premise is he is 6 years older. Being 6 years older than someone's DOB can never change. So, how is she 5 and he's 10? That's only 5 years older....can't make sense out of this.
Dan is officially 6years and 1 minute old to be twice Ann’s age !! That’s the real answer no matter what the given choices are !!😂 19:26
Let's just pause to realise that they both have the same birthday and it is whenever you read this question.
ANN's is 6years old Dan is 8 year's old
Dan's 10, Ann's 4
Dan is 10 and Ann is 4
12/6 = 2*1
What a long drawn out way of solving a very simple problem.