Ann is 3 times older than her brother. In 4 yrs, she will be twice as old. How old is her brother?
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- เผยแพร่เมื่อ 26 ก.ย. 2023
- How to solve an algebra age word problem step by step.
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Right now Ann is 12 and her brother is 4. That’s 3x older. In 4 years Ann will be 16 and her brother will be 8. That’s twice as old.
I agree 100%!
I agree 💯% as well! 👍🏽😊
Right.... but the guy talks too much!! he talks , talks, and gets people confused.
@@cic-jakevanddalgeemyers.2739he charges by the hour, that’s why.
I did the same instantly
😳 I'm 64 yrs old and trying to stay sharp. What a challenge 😬thank you for your wonderful videos. I watch them often.😊
Mr. TH-cam man, you’ve ignited my second go with math. I appreciate you; your contribution to society has not gone unseen.
Four years
Yes it took me on a journey. Reminded me of flying from Australia to LA. long but eventually I got there. 😅
I am 78 years old. I don’t remember learning any of this in high school. It’s so interesting and I am learning a lot. Thank you.
As am I!
I'm 70, educated in NZ, and we had this.
Maybe you were too busy smoking dope,it was the seventies.
You didn't miss much
I never learned this type of problem when I was in school. I prefer the mole to mole ratios in chemistry...haha...I actually appreciated organic chemistry a lot more my second go around with that :- )
I chose Ann's age variable as A and the brother's age variable as B. This helps by eliminating the X and Y translation to their names.
Love the channel but a word problem depends on language. As written, it clearly states Ann will be twice as old. It does not say twice as old as her brother but twice as old (as she is now). I solved it the way it was written. I do love the channel, and the math teacher who creates it. There is an inherent logic in language that cannot be denied legitimately.
I thought we were talking about Ann being twice as old.
I don't understand why you would presume the second sentence would deviate from the comparison (to her brother's age) in the first sentence though?
Since he didn't specify the comparison in the second sentence as being a comparison between her ages at two different times (by putting "as she is now" at the end of the second sentence), then it seems the logical conclusion would be to presume that he's comparing her age to her brother's age in the second sentence as well...
A period between these two sentences doesn't change the train of thought between these two sentences, unless otherwise specified, I would say.
Unless you WERE thinking that?
How did you read it?
I agree and I came up with 18 months old as a result.
It's trickery and we wonder why a child would fail it.
I solved this instantly without messing about with algebra. I also did what I used to do in school: reinterpret the words to match what was actually intended.
You right. simply read the question and answer it with logic, not math.
I agree and did the same with this problem. That said , it explains the process which can be applied to much more difficult (college level) math. I need a refresher in proper grammar though 😂
Twice even 😲 incredible! Who needs “math”
Sure, you can easily deduct that because they are small, simple numbers and the reductión was from 3 times to two times. I mean, in 4 years 3x became 2x, x has to be 4. But for more complex calculations, you definitely need algebra.
I would expect a 6 year old to be able to answer a question this simple without algebra very quickly but hey kudos to you for being able to do math
I have to say although I understand what is being asked for in this problem, I have a MAJOR problem with it's grammar. If Ann if 3 times older than her brother who is 4, then she would be 16 because 4 + (3 x 4) = 16, because she is 3 times "OLDER", which means 3 times his current age plus his current age. The correct wording should be Ann is 3 times "AS OLD". As you can see in the second sentence in the word problem the grammar is correct since they are using "twice AS OLD".
Let Y be Ann’s current age, and X be her brother’s age. The first statement gives us:
Y = 3X
The next statement tells us in 4 years:
Y + 4 = 2(X+4)
If we substitute 3X in place of Y, we get:
3X + 4 = 2(X+4)
3X + 4 = 2X + 8
X = 4
No need for Y. Let the brother age be X. Then 3X=2X+4, thus X=4
I love all the problems I can do, that you provide, as mental math. Thanks!
At present: A = 3 * B
In four years: A + 4 = 2 * (B + 4)
Substituting for A in the second equation we get: (3 * B) + 4 = 2 * (B + 4)
Simplifying we can write: 3B + 4 = 2B + 8
Subtracting 4 from both sides we get: 3B = 2B + 4
Now, subtracting 2B from both sides we get: B = 4
And substituting the value of B into the first equation we get: A = 12
Cross-checking we plug the values of A and B into the "in four years" equation and get: 12 + 4 = 2 * (4 + 4)
Simplifying, we get: 16 = 2 * 8
QED
better phrasing would be in 4 years she will be twice his age
I would like to say how much I enjoy your videos. Your explanations are crystal clear. Together with your soothing reassuring voice you make the problem easy to follow.
I am an English language teacher myself and have been living and working in Italy for many years.
I was not good at maths when I was growing up in London, but strangely enough I always liked it. Probably due to my enthusiastic Indian maths teacher, Mr Sharma.
I do not think that you are obsessive, but I believe that you have a passion for your subject.
I am subscribed to your channel, and I give you a like every time. Please continue to make videos. I will recommend you to my Italian students. They will pick up some good English and I am sure you will help them to sort out any difficulties they are having with their maths. All the best and have a nice day.
Ann is 12, her brother is 4.
Great video!
That said, it seems a bit counter-intuitive to start with Ann = 2* Brother, seeing as that's starting from the end, and also working towards finding out his age in the future, not "now" as is requested.
Seems like this would better translate to the following:
Ann = 3*Brother // now
Ann + 4 = 2 * (Brother + 4) // in 4 years
So, replacing Ann on the lefthand side of the 2nd equation using the 1st one, and expanding the multiplication on the right side, we get:
3*Brother + 4 = 2*Brother + 8
Which leads to:
3*Brother - 2*Brother = 8 - 4
And then:
Brother = 4
And that's the answer for his age *now*. Of course, everyone has different ways to approach problems, but for me, I find this to better match how the problem is presented.
I simply looked at this through LCM (lowest common multiple) - the number 4 is key to my thought process.
She is 12, and he is 4.
12 is 3 times more than 4, and in 4 years, she will be 16, whilst he would be 8 (twice his age in 4y).
I had this solved in 30s, before the video started. And, I was right.
Multiple ways to get to the right answer!
I solved it while on my way to clicking on the video. Stupidly simple an they are going to make a big complex algebraic problem out of it.
@geraldpatrick9463 I do appreciate though how the algebraic processes were explained. Not everyone has an aptitude for mathematic concepts.
I did it exactly the same way in way less time than it took him to explain the algebra behind the math. I wonder how long it would take him to do the two train one. Pax
I hope you don’t mind my having a little fun with this but “ twelve is two times MORE THAN four( not three times more)”😝😜🤪
@@light279 New math?
I liked that problem, I figured it out before you had time to set up the problem, thanks for sharing this problem with us.
Thank you for the vid.
Some math instructors want to see every step or points will be taken off. This was very clear.
I have five younger brothers, so I figured it out by using the math in my personal life, and came up with the correct answer, in spite of your lack of English skills.
'In 4 years she will be twice as old.' could be read two ways - that Ann will be twice as old as she was, OR that Ann will be twice as old as her brother.
I feel like you take eons to explain everything. But I so very much wish that I had a teacher like you 40 years ago when I took algebra. Thanks for your work and for your videos.
What these type of relative age problems deal with are differences in age multiples of the older person between a specified number of years. The general formula can be described as (ax - bx) = d. 'x' represents the age of the brother which is what we are trying to solve. 'a' is the current multiple of her brother's age (how many times older she is currently) and 'b' the future multiple of his age. 'd' represents the difference in years (ie: how much time will have passed) between the the first and second multiples. You could also write this in its factored form: [ (a - b) * x ] = d as long as one doesn't mind an extra set of brackets! This is easier to simplify down to: x = d / (a - b)
This generalized equation would also work for the less neater variety of inputted data, including non-integer multiples of age. If the problem were described as Anne being 7.5 times older than her brother currently and in 9 years she will be 4.25 times older then the equation of: 7.5x - 4.25x = 9 would simplify to: 3.25x = 9 yielding: x = 2.77 (rounded to two decimal places). The decimal portion would just be an expression of a part year, approximately three quarters. Thus Anne's brother for this scenario would be just a fraction over 2 3/4 years old currently.
Love the comments on the wording used. I got the answer in about 15 seconds in my head. (always been good at math). Funny about 3 times older is the same as 4 times the age and that she would be twice as old (as herself now???) With that said I got the gist of it and chose bro as age 4.
I am ok at math(s), but this channels makes me smile, re-teaching me math(s) so I can help my kids when the struggle with their home work. Big thanks from the other sid of the pond.
You mean they still do homework; my grandson is in grade six and the only Home work he has ever done was during lockdowns. Pax
@nf_100,
Why did you use four question marks there? It’s one question mark not four.
She is 3 and her brother is 1. Their birthdays are both on feb 29, and she will be 4 and her brother will be 2 in 4 years from now.
THANKS!WE WERE ABLE TO UNDERSTAND CLEARLY!!.daniel & miss cirila.CANADA.
Thank you for your videos. It is great for learning. I hope you do videos forever I will definitely be supportive. Also I hope you do basic math as well. I love word problems they help you think.😊
Thank you for this video
Wow, after taking algebra 3 years in high school 30 years ago and failing all 3 times, I'm terrified of algebra,, I'm back to school now at the age of 62 I enrolled in college and I'm working on earning my bachelors degree in game art, one of the classes I'm required to take is college math, and I'm terrified that I'll fail the algebra portion. I've been watching all your videos and really paying close attention to your process and finally for the first time, I understood the process of the algebraic solution for this question, I actually guessed the answer correctly by doing deductive reasoning and came up with 4, but as you started to create an equation out of it I started thinking like you and I was ahead of where you were going the whole time and I'm so happy that I can now solve this problem by algebra and maybe by the time I have to take my college math course I will have learned enough from you that I won't fail. My goal is to graduate with a 4.0 gap and I'm on my 6th course right now and have a 4.0 gpa. We take one class for 4 weeks then we start the next class so I have 27 months of classes until I reach my degree and I will be thrilled if I can get an A in college math, I already aced psychology and college English composition and I have received 2 directors award submissions for having the highest grade in my art1 class as well as my technology and communications in the media industry course. So I'm on the right path, right now I'm studying 3D foundations and having to learn how to use different 3D animating and sculpting software programs and it is all based on geometry which because I couldn't pass algebra I never got to in high school. So I'm having to learn not only geometry and new software I'm also having to learn how to use a windows of from a Mac which I just started using the Mac in my first course 5 months ago after only using an I pad for 10 years and its been 15 years since I used a pic. I am taking a crash course on LinkedIn on how to use windows 10 and 11 and have been learning everything to do with a computer for 2 days now. I'm really excited to learn how to use a pic because when I was originally in college in 1982 I was asked if I wanted to take a course in the new computer lab and I looked in the room at those old bulky monitors with there little screens and green letters and I said no thank you, I think computers are just a fad like everything else in the 80’s and would never take off just like 8 track players. Boy was I wrong and as an artist it has been a battle between me and computers for 40 years, for the most part I could always beat computers and draw faster and more accurately than a computer could but as of the last 10 years computers have been catching up and beating me, and so I decided that if I wanted to survive as an artist I was going to have to embrace the computer and learn how to use them. Now with AI taking off at such a rapid pace I may become outdated before I finish my degree program as AI is advancing beyond the technology of the software I'm currently being trained on, so I'm learning how to embrace AI. And I know if I want to survive in the future I'm going to have to adapt to using AI. Technology as part of my artistic process because if I don't use it, I will just get left behind from the younger people that are using it. So at the age of 62 I'm staying up to date with technology and looking forward to opening my own home studio where I can work as a freelance remote working artist for the game in G art and design business. That's my goal for my golden years. I'm already retired but I'm looking for a late life career and not retiring permanently until I'm 90. I think I still can put another 30 years into a career .
I solved this in seconds. No algebra involved.
Inspiring this new generation
You can do it a bit different in how to express the ages and then do the algebra. But it is essentially the same thing you did. I know some people, find this a bit easier to visualize.
Ann is the right side of equation and brother is the left.
Today: 3x=y
In 4 years: 2(x+4) = y+4
2x+8 = y+4
I then substrates the future age from todays age (you can to todays age minus future age as well if you want) to get rid of ‘y’.
3x- (2x+8) = y - (y+4)
So i then get x-8 = -4
X= 4
I got by trying different numbers.
I like this guys voice.
Being an old person and not knowing algebra, I did it the grade school way:
1x3=3, +4=7 (not divisible by 2)
2x3=6, +4=10 (2+4=6 and 10/2 is not 6)
3x3=9, +4=13 (not divisible by 2)
4x3=12, +4=16 (4+4=8, 16/2=8)
And I agree with other posters... the grammar left this question possibly confusing...
This is why I feel the proficiency tests given before 2014 where unfair. Maybe putting it into your own words would help....after you fully nunderstand what the problem is saying.
1:3 2:6 4(+4):12(+4)
I don't normally post in your comments, but I have to say this... Your word puzzles are written concisely! Keep up the good works!
Here brother is 4 years old. He will be eight, and she will be sixteen in four more years!
Love you mathematical puzzles!
This is why i love math! I had the right idea, just made one goof, which is all it takes. It really jiggled my memory cells. I love this. I have a problem for you i have not been able to solve. How do i send it to you? When we go to the big city, i have 5 hours driving which gives too much time to think of things and pit stops. So, i ask questions about my encounters and time etc... When i mention the math questions to others, they think i am nuts. No, just very curious, and they aren't. The hav e their fun, i have mine. After i took Algebra, i even saw it in a dance the kids were doing at a Spanish Club dance. There was no oneto talk to about it. I wanted to write it down, but no way to do it, and later, i could not remember the pattern. I asked my math prof who had figured these things out (history), and what is the practical application ? She said those were questions for greater minds than hers. I thought it a rather sad answer. Later i dated a guy who installed wood stoves. He used it to figure out the pitch of the roof so he could order the correct parts. I imagine he may have needed it for other installment issues, too, but that is what learners need in order to comprehend how and why it works. Maybe they do that now. '93 was my last class. Thank you.
After pausing the video I of course overcomplicated this thing as a pair of equations:
a = Ann's current age
b = Brother's current age
Initial Equations:
a = 3b
I solved it before watching the video. Had to go back about 50+ years to remember how to do this. HOWEVER, this demonstrates my problem with how we teach math. No one will ever use algebra to get this answer. They will just ask Ann’s mom how old her brother is. So to effectively teach math we need real world problems, not made up riddles. I recall learning binary math. Remember how old I am (you can approximate my age based on the information I have supplied). I asked my teacher, “Why would anyone use a math system with only 2 number? Especially when they have 10 fingers?” Her answer was, “It’s in the book and we have to learn it.” It wasn’t until 10 years later (more help estimating my age) when I got a real job working on computer terminals that I realized the practical value of the binary system. To this day computers function on based on 0s and 1s. Would have been helpful to me to know that in class. I would have seen a purpose for the math. I was not one of those students who was challenged by the problem itself. If it didn’t have practical value, learning it was pointless to me. So the big question that I still don’t know the answer to - what is the practical application of this problem? Real world useful example?? Serious question, but I appreciate the challenge to remember what I learned in the last century. Good video.
Thanks
Ann's 12 now & her brother's 4. In 4 years she'll be 16 & he'll be 8. Easy again.
Loving this ❤
Another good example of using the Gaussian elimination or matrices techniques.
I REMEMBER that now! THANKS!!
I feel like we need a reading comprehension lesson rather than a math lesson. This is a very easy problem to solve actually. You will get two "correct" answers, depending on how you interpret the "In four years she will be twice as old".
The problem in the interpretation is that there is a "assumption" made rather than sticking to the logical statement.
"In four years she will be twice as old" is ONLY logically referring to her own age. There is no statement in this sentence correlating her brother. Therefore the solution and work shown in the video is incorrect.
Yeah when I read the sentence, I thought it was saying 'she' would be twice as old. Nowhere does the sentence refer 5o her brother. Then I listened to him talking. The sentence isn't worded the correct way.
chaecoco2 writes: “You will get two ‘correct’ answers, depending on how you interpret the ‘In four years she will be twice as old’.”
Oh right. You mean that the sentence can be interpreted not only as in A, but also as in B.
A
In four years she will be twice as old [as her brother in four years].
B
In four years she will be twice as old [as she is now].
I have to admit that I interpreted the sentence as a colloquial shortening of A (see the formalization in my original post). But both interpretations are actually possible. The text is simply not clear at this point. Therefore the problem can only be solved if you first state how the sentence is interpreted. And then the solution is valid only under the condition of this interpretation.
I think the tutor should post the video again with clear wording.
I hereby provide the solution under the condition of interpretation B (for A see my original post):
x = current age of Ann
y = current age of Ann’s brother
(a) x = 3y
(b) x + 4 = 2x
x - 2x + 4 =
x - 2x = -4
-x = -4
x = 4
3y = 4
y = 1⅓
CONTROL
(a)
4 = 3 ‧ ⁴/₃
4 = 4
(b)
4 + 4 = 2 ‧ 4
8 = 8
Best regards
Marcus 😎
1:3 2:6 4:12.
You don't need to subtract 2X from both sides. Move the positive 2X from one side of the equation to the other it becomes negative. Any time a term crosses the equal sign it changes to the opposite; positive becomes negative, multiplication becomes division...
This is the way I was initially shown to do it when I was a junior in high school, and it is the correct way. It involves fewer steps and makes you think about what is happening. I was shown the right way first but later, the instructors tried to poison my mind with the incorrect way that involved unessecry steps.
Wonderful teacher. I had these skills once upon a time because my high school teacher was brilliant but that was 55 years ago. Thank you for bringing this back.
Will she be twice as old as she currently is or twice as old as he is in 4 years? Assuming the latter, A=3B and A+4=2(B+4), so 3B+4=2B+8 and Ann’s brother is currently 4.
Correct
That's the way I did it too.
3X=2X+4
@@jwsmock84This is the way I did the problem
Im 75 and i love these problems. I nver got them wrong back then in school !
Do you know when I ran into problems like this at school I found them almost insolvable truly impenetrable, and hey guess what, I still don't understand; unlike most posts here. There are obviously there must be rules that I didn't get taught or was expected to intrinsically know. I will watch it again
I love your videos - genuinely I do. But you need to more carefully phrase the second statement. It says “In 4 years she will be twice as old”. It does not say “twice as old as her brother”. One can say it is implied, but then that could have been flipped around to say “Ha, I didn’t say twice as old as her brother.” Probably won’t agree, but I still love your videos.
No doubt! I mean, I assumed he meant “in four years she will be twice as old as Kenny G. “
So confusing!
I understand but as you acknowledged,the implication is that her age is being compared to her Brother's age:)
I took it as SHE would be twice as old! Like many have said, better wording would prevent misunderstanding!
I solved it correctly!
I had a Mohawk in 1983.
I have a Mohawk this morning in 2023.
The Mohawk makes ALL the difference in my maths skills.
I actually did guess and test and got it on the first try. When thinking algebraic I used two variables and two equations.
Never went to high school no algebra got a machine shop job 1966 OMG Did it till 2020
School of Hard Knocks
( you sure make it easy to understand )
Thanks so much 🙏 I'm to old to use any of it
2 things: First, I like to use variables that reflect the problem. I.e., let A = Ann's age, and B = Brother's age.
Second, translate each sentence into an equation: Ann's age is 3 times Brother's age--> A = 3 x B.
Sorry, lost my position. A+4 = 2(B+4). Then substitute 3B for A.
Fascinating
Wow! This word problem was real tricky like a riddle being told to me. But the requested answer being ask for the brother was a lot simpler than I had thought. The answer is, the brother is now 4 years old.
An additional thought: I'm curious to know about the sister's present age as well
If the sister is twice as old as her brother, does this make her age 8 years old or 12 years old in the present time since she is still 3 times older than her little brother??
I'm thinking more towards that the sister is no longer 3 times older, but is (now) twice as old as her little brother in present time.
So...now, sister is 8 years old? Am I wrong?
I solved the equation by multiplying 3x4=12 for ann”s years and divided 3/12 =4 for her bothers year. if we add 4
he would be eight and she would be 16.
the same scenario would have of it were 3x5 years older 15 means he is 5 + 5 years
she is 20
and he is 10.
or 3x 6 years she would
be 18 and he would be 6
in 6 years they would be 24 and 12.
I really dont remember how to do linear algebra.
the same for 7x3=21 +
7 is 28 /2=14. But I will practice the hard algebra way so I can remember.
I remember in the 80’s in grade school
doing the CAT’s . I got a perfect score of 12.9 going into high school, but I did not understand algebra’s formulas. Somehow I had my own fomula’s with regular math and blocking in my head to get the answers really fast. I am a pre-senior today a d I want to know all of the formulas
and become a mathematical genius before I turn 60.
How old
am I today? 😂😂😂
❤❤❤❤❤I LOVE IT SO MUCH AND KEEP IT UP
18 min to get to the ans yes. It holds you in anticipation. It's mind blowing excitement. We want more.
This is fun!
I thought it would be easy. Then I got confused. Now i get it. thanks.
This isn't too bad; (i) 3b = a and (ii) a + 4 = 2(b + 4). Solve, giving b = 4. a being annes age and b being her brothers age.
Ann is 12 Brother is 4 system of equations a=3b a+4=2(b+4) use substitution.
Shouldn't the first sentence be constructed "Ann is 3 times as old as her brother?"
At Four minutes of the Clip, thats when He starts to Teach, then loses His chain of thought, then comes back 😢. Still i subscribed and learned something, even tho He still loses his chain of thought.😊😊.
My equation: 3(X)=2(X)+4...solving for X yields: 3X-2X=4; thus X=4yrs. old.
I hated story problems when I was in school! Sure wish you had been around then. Maybe I wouldn't fear math so much.
I came up with the answer "4", but I don't know how. I just figgered it out.
Same, but I'm watching the whole video because it's better to learn the principle behind it.
@gerontodon I watched the whole video, too. I always did better with story problems than with equations in school, and it was frustrating to me and to my teachers. I could get the answer but not understand how.
No wonder I was never good at word problems
4. Did it in my head in 15 secs.
15 seconds solved in A.I. head and 10 minutes to construct problem, differently mind you.
3X+4/2=2X, ....... 3X+4=4x......or 4X=3X+4......4X-3X=4.....X=4
Brother=4 years old
At 15:55 you should subtract 4 on both sides, you are missing the minus sign on the right side of the equation. Greetings from Switzerland
16:12 / 18:38
Ann is 3 times older than her brother means she is 4 times as old so, if you mean she is 3 times as old, say that. the answer is 6. when the brother was 2 ann was 8 (4X) 4 years later she is 2X6, or 8+4 or 12.
Hello everyone,
here is my solution, without watching the video or reading the other comments:
x = current age of Ann
y = current age of Ann’s brother
(a) x = 3y
(b) x + 4 = 2 ‧ (y + 4)
Subst. (a) in (b)
3y + 4 = 2 ‧ (y + 4)
3y + 4 = 2y + 8 | -4
3y = 2y + 4 | -2y
y = 4 | Subst. (a)
x = 12
CONTROL
(a)
12 = 3 ‧ 4
12 = 12
(b)
12 + 4 = 2 ‧ (4 + 4)
16 = 2 ‧ 8
16 = 16
qed
Best regards
Marcus 😎
Its obviously recommended to do it the algebraic way, but you can actually get to the answer pretty quickly via guess & check.
For starters: We know that the brother must be an even number of years old. If he was odd, the math becomes impossible. To prove that:
Suppose the brother is an odd number of years. If Ann is three times older, that means she is also an odd number of years old. Because multiplying three [odd] by any other odd number will always return an odd value.
So if the brother is odd, Ann must be odd. But here comes the issue: In 4 years, Ann needs to be TWICE the age of her brother. an odd number plus an even number will always result in an odd number. So if Ann is 7, in 4 years she'll be 11. 11 does not divide into 2. Not does any other odd number. Therefore, her brother cannot be an odd number of years old currently.
From there, let's proceed to guess & check. You're welcome to try a larger number for her brother's age, like 20. That would put Ann at 60. In 4 years, they'll be 24 & 64. That's not particularly close to being twice as old. Still much closer to three times as old, really. The larger you go in the brother's initial age, the worse this problem becomes (and sadly, the less likely it is for Ann to still be alive.)
So its easier to just start from 0. That will fail. 2 will fail. Hey, 4 works.
Obviously this is a long way to get to the same answer. And arguably even requires a mind that is already familiar with math, to the point where doing it the right way is simpler for that person anyway. But this was actually how I went about it since I didn't have pencil and paper to write everything else down in front of me, haha
The problem is that you did not proof that the solution becomes worse for values larger than 4. You will have to proof that for a value higher than 4 the situation will be more than twice the age. You write that as a statement without proofing it.
@@henkhu100 guess & check is inherently a pretty sloppy method. So yeah, I write it as a statement without a proof, but it seems like a very safe statement. For good measure, you could also check what happens if the brother is 50. Ann would be 150. In four years they'll be 54 and 154. That's even further away from the 1/2 mark than if we went with the bro being 20. It's pretty clear to see that bigger numbers perform worse. Don't need a proof before diving into the easy guess & check.
You can say there was a problem in my method, but my mathematical instincts guided me correctly, as this is precisely how I went about solving it. While not proven, it does seem pretty obvious that (b+4)/(3b+4) will net an even smaller number as b increases.
If you want a proof though, I think calculus would do it:
we can take (x+3)/(3x+4), painstakingly take the derivative of it. Or. Plug it into google and get:
-8/((3x+4)^2)
So the only critical point is x=-3/4.
So if I plug 0 into that derivative, I get -8/16 = -1/2. Therefore this graph is always getting smaller for all values of X bigger than 0 (-3/4, actually, but we don't need to worry about ages less than 0) in the equation: (x+4)/(3x+4). So as X grows, y gets smaller.
Around 7 seconds, genuinely and I enter my 8th decade in London, next yesr:)
In the end, everything comes down to basic math!! Doesn’t matter what the concept is!!
this one was easy to reason out without algebra. We already know the answer has to be an integer in the range of life span of humans. So, first try the simplest answer. Three time older could 1 and 3, 2 and 6, 3 and 9, etc. but it also can only be double in 4 years. Try 4 because 3 times 4 is 12 and adding 4 to both is 8 and 16. Easy peasy. But most real world problems are not this simple and usually don't have to be integers.
Withh the giveninformation,you get 2 independent equations.Let the age of Annbe a and the age of hher brotherb, then you get:
a=3*b
a+4=2*(b+4)
If you substitute a withh 3*bin thhe second equation, you get:
3*b+4=2*(b+4)
3*b+4=2*b+8
b=4
With this result, you get from the first equation: a=3*b=3*4=12
So Ann is 12 years old and her brother is 4 years old. in 4 years, she will be 16 yeas old and her brother will be 8 years old.
4
Somehow I'm able to look at math problems and intuitively know the answers. I don't know how I'm able to do this but it's something I've always been able to do. However that isn't actually the solution to the question. The real solution is the procedure and equation that allows you to solve it and that's something I've always had trouble with. In school despite having the correct answers I often got the problems wrong because how I solved them wasn't correct. Everyone always said "he's really good at math" but I consistently had a C average. lol
I did it a little bit different: Ann = x, Brother = y
Today x = 3y, in 4 years x = 2y + 4 ==> 3y = 2y + 4, ==> 3y - 2y = 4, ==> y = 4
Her Brother is 4 years old today.
If you say Ann's age is 3x.
The wording to this would be:
Ann is 3times as old as her brother
a=3b;
a+4=2*(b+4)
solve for a and b...
Plus and minus fractions would be interesting.
let Anne's age = a and her Brother's age = b then we simply have simultaneous equations
a = 3b and a+4 = 2(b+4) which simplifies to a + 4 = 2b + 8 and then a = 2b+4
Subtracting the simplified second equation from the first gives 0 = b - 4, therefore b = 4. There's the answer.
Putting back in to double check, a = 3b = 3(4) = 12. In four years Anne is 16 and her Brother is 8. All good.
The key to every solution is the proof that it worked. One missing link could be filled in here by testing the result and filling out the table to check your work.
I knew in gradeschool that if the teacher would give me one hour and answer my questions (in my time, not conscript me in a discracting crowd) that if one is..able to pay UNDISTRACTED attention, you get this stuff pretty fast. I urge people to try ONE or TWO of these videos, to remember waht it was actually like to be harassed into thinking you can't actually think clearly. Then, you may choose to speak to your phone to do it, but you will see what mostly ALL schooling is really for. This ability is of use, yes. However, intimidation makes teaching a tool for social control. You pass a test, its no gift.
I enter my 8th decade in London next year and did it in 7 seconds(approximately),genuinely.
The ages now are Ann 12 brother 4
Key point: Moving the variables to the left of the equation to have only numbers to the right. Got it!
You only gave the rule without explaining the logic of it though. If one wants to understand what one is doing one needs explanations. ;)
But why substracting 2x and not adding it both sides instead. :(
Because we need to get rid of the variables on the right side of the equation.
You kind of jumped the gun a bit at this crucial point of the solution.
That's why some may want to do video games instead.
Respectfully!
I need all details explained!
@@hulamei3117 That's what I asked for but I don't think answering our questions is part of the deal. I can live with that.
Ann is 12 now and her bro is 4. In 4 years Ann will be 16 and bro will be 8. A=3b. A+4=2(b+4) so 3b+4=2b+8 giving b-4=0 so b, her brothers initial age is 4. Ann is 3 times that so she initially 12. In 4 years she will be 12+4=16 and bro will be 4+4=8 which is half of 16.
My algebra skills were not working on this one to set up the formula correctly. So I try old and aired it. And I got it correct. My algebra came out too old.
You left off the negative sign when you placed the 4 under the positive 8. Your diagram shows 8+4=12, but it should have shown 8-4=4.
Did this one in my head without algebra butstill fun.
4 years old and therefore she's12.
In 4 years :
4+4=8
12+4=16
So she'll be twice as old.
I did it in less than one minute, mental arithmetic.
So did I - no maths involved. Just went through 2 scenarios.
Same here. I did several iterations in my head, until the two ages had the correct relationship (as described in the question).
But in an exam, I would use algebra!
I think that the wording should be …Anne is three times AS OLD as her brother ( and not three times older than her brother ).Three times older means that she is presently four times her brother’s present age.
If she is three times older, then how does the equation suddenly change to her being 4 times older?
Three times older than brother = 3×X
Only after you calculate the additional four years (for both siblings), and then subtract, that is the only time 4x comes into consideration at all.
This question is more about reading comprehension than math...
genau deswegen ist die Lösung ja: 1, exactly therefor the only correct answer has to be: 1@@iane1335
12 & 4
Her brother is 4 and she is 12. In 4 years he'll be 8 and she'll be 16. I just guessed... I knew her 4 years later age had to an even number... and I guessed 18, but that was a little off and my second guess was 16 and that worked.
Took me about 45 seconds to find the answer using an Excel table 😊
But then again this was only possible as I was sure the brother was younger than 60. ;)
Could it be argued that "three times older than" could be interpreted as "3x + x"?
I think a more clear wording would be "three times the age of" if it is to clearly imply "3x"
Since "100% = 1x, thus 300% = 3x" and "100% larger than = 1x + x, thus 300% larger than = 3x + x"
I see two solutions for the problem statement. The one you have performed here assumes that she was to be twice as old as her brother in 4 years. I read it as Ann being twice as old herself. The problem statement is not clear so the solution must have two possible solutions. Can you write a possible formula for the second solution?
I had to do it systematically from 1 up:
1 x 3 = 3 so 1 + 4 = 5 and 3 + 4 = 7 nope
2 x 3 = 6 so 2 + 4 = 6 and 6 + 4 = 10 nope
3 x 3 = 9 so 3 + 4 = 7 and 9 + 4 = 13 nope
4 x 3 = 12 so 4 + 4 = 8 and 12 + 4 = 16 yep!
I guess I did solve it using algebra. I just didn't realize that I was looking at her brother's age after four years.
My equation was:
1/3 A + 4 = 1/2 A
3x=2x+4 and x=4 this is my short cut do the math in your head I did this when I took algebra almost 50 years ago.
I just picked a few numbers in my head. Her brother is 4 and in 4 years he will be 8. The sister is12 now and will be 16 in 4 years.