Algebra SYSTEM WORD PROBLEM - Let’s solve it step-by-step...
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- เผยแพร่เมื่อ 6 ส.ค. 2024
- TabletClass Math:
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Math help with solving an algebra word problem involving systems. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at tcmathacademy.com/
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Usually, when I face problems like this, a weird thing happens in my brain where I experience a sensation of vast empty space between my ears. Alternatively, I experience a vast, arid desert, devoid of dunes or wind or anything. It is “I have no clue” but on more steroids than Pete Rose ever saw in his whole lifetime. It is just a pure, unadulterated emptiness. But this, Mr. TabletClass Math Man, this gives me hope. A slight glimmer of a distant star in the vast blank universe of my math brain. Thank you.
Are you taking a Geophysics or geology course?
I got this! But I wouldn't even try if I had not watched previous videos. Great stuff to start the morning.
What a convoluted way to solve a really simple problem!
MR. TabletClass Math, thank you for another fantastic video/lecture on Algebra System Word Problem in Algebra One. These word problems are fun to solve bro.
I discovered a few years ago I'd forgotten how to do simultaneous equations and it really bothered me. Thank you so much for the clear explanation - I'll get cracking on solving a few and come back to your next tutorial that interests me. I loved geometry which was dropped from the curriculum as I progressed up senior school, so it'll probably be those tutorials first.
Only he didn't use simultaneous equations. He just abandoned that halfway through and went to the substitution method with only one equation.
Sorry, I know it's been two years, but if you're interested in how this _is_ done with simultaneous equations (or a system of equations, as he calls it) just reply and I'll show it.
Yeah, teacher. Thanks for the help! I was able to do it myself though. You are very funny. SUBSCRIBED!
Thank you for the clear explanation of how to solve the system and solve for x.
I know it's been two years, sorry, but he didn't use the 2-equation system to solve this. He just did a substitution to make a single equation. It worked, of course, but he completely dropped the system approach.
Let x= the number of small cans sold. Since there were twice as many large cans, we use 2x to represent the number of larger cans sold. Inserting prices and total cost: 8.95x + 2x(15.95) = 694.45. 8.95x + 31.90x = 694.45. 40.85x = 694.45. x = 694.45/40.85 = 17. x was the number of small cans sold, which is 17. Reintroduce prices: 17 X 8.95 = 152.15. Subtract from the total (694.45): 542.30 is the total amount of the large cans. Divide: 542.30/15.95 = 34 large cans.
Now, how many square feet will the total wood stain cover? (Trick question, there's no way of knowing without volumes of each can size, as well as coverage for the type of wood stain sold. Solution: call Lowe's.)
Just like coins, I used the stack method. I merely stacked two large cans, with a small can on top. I added the values, $15.95+$15.95+$8.95=$40.85. $694.45/$40.85=17 stacks. From there, it's easy to see, that there were 17 small cans, (one in each stack), and 34 large cans. (two in each stack) I guess you would call this "Prealgebra".
Ratio of cans sold is 2L:s (units) unit price is (15.95*2) + 8.95 = $40.85
Total sales of $694.45/Unit price of $40.86 = 17 Units
17 * Unit ratio of 2L:s = 34 Large + 17 small cans
Do you have something for the customs and boarder patrol math ?
What is the link to this video?
MR. TabletClass Math, thank you for another fantastic video/lecture on Algebra System Word Problem in Algebra One. These word problems are fun to solve.
Nice !!!!!!!!!!!!!!!!!!!!!!!!!!!!
Try X x 8.95 + 2X x 15.95 = 694.95
Gives 17 small and 34 large, or am I wrong?
Why did we need y at all when it would be 2x at the start?
When there's two unknowns then to solve requires two equations.
First Step: assign variables:
number sold
L => number of large cans
S => number of small
price each:
P.L = $15.95
P.S = $8.95
Total Sales Revenue
T.S = $694.45
Step Two: write two equations from the problem:
eq.1: 2S = L
eq.2 T.S = $8.95S + $15.95L
694.45=8.95S+15.95L
Step Three: substitute eq.1 in eq.2
694.45=8.95(S)+(2S)(15.95)
=8.95(S)+31.90(S)
=40.85(S)
(S)=(694.45)/(40.85)
S=17
ans.1 small cans # = 17
from eq.1: 2S=L
L = 2S
L = 2(17)
= 34
ans.2 large can # = 34
VERIFY:
eq.2 694.45=8.95S+15.95L
$694.45
=?$8.95(17)+$15.95(34)
=?$152.15+$542.30
=❤ $694.45
Seems like this should be simpler. 8.95x + 15.95 * 2x = 694.45
X(8.95 + 31.90) = 694.45
I guess I learned to do the the substitution as part of the initial setup. Long ago
I never took anything but general math and I regret it.i'm not so sure about the 2 x.isn't this just making x equal 1 because the large cans cost less than 2x the small cans. I just took the cost of 1 small added 2 large which is the cost of a set of 3.then divided the total by this which gave me 17 sets.x1 for small x2 for large
In Scotland we call them Simultaneous equations
The answer is 34 large and 17 small when 40.95x= 694.45.
someone told me if you know algebra high school math college alegbra be easy is that so.
You didn't actually use the system. You just did a substitution to make a single equation.
If you used a system (what we called simultaneous equations when I was in school) then the equation 2x = y would become 2x - y = 0, and then go from there with both equations.
Multiply the top equation by 15.95 to get 31.90x - 15.95y = 0.
Then add the equations. You'll get 40.84x = 694.95.
34 large to 17 small cans
34 large and 17 small.
B is number of big size (large) T is number of tiny size (small)
15.95B+8.95T=694.45 and B=2T
are the two equations
factor first equation by .05
(15.95B+8.95T)/.05=694.45/.05
(15.95B/.05)+(8.95T/.05)=694.45/.05
319B+179T=13889
Do substitution
(319*2T)+179T=13889
638T+179T=13889
817T=13889
17=T
B=2T
B=2*17
B=34
check
15.95*34=542.30
8.95*17=152.15
add the two 542.30+152.14=694.45
Okay ... So I am doing these for fun cause it's been 40 years since I studied all these and it's nice to refresh. But I used to do these things without all the steps listed out.
starts at 12:13
Great explanation of the math part. Foreword much too long
If we let the number of small cans sold = X the number of large cans will be 2X
So ... I think that the equation here is 8.95X + 15.95(2X) = 694.45
8.95X + 31.90X = 694.45
40.85X = 694.45
X = 694.45 / 40.86
X = 17
17 SMALL CANS 34 LARGE CANS
This is what I thought. Why bother with a y variable when you can just use x and 2x?
173651
Never use 2 unknowns when 1 will suffice.
7 sold of small cans and 14 sold of large cans
This is painful
First step: Set your variable to be your answer.
Let x be the number of small cans sold.
Then the number of large cans sold is 2x.
Second step: Construct your equation.
The cost of the small cans is x * ($8.95)
The cost of the large cans is 2x * ($15.95)
The total cost is thus x * ($8.95) + 2x * ($15.95), which equals $694.45.
Third step: Solve.
x * (8.95 + 2*15.95) = 694.45
x * (8.95 + 31.90) = 694.45
x * (40.85) = 694.45
x = 694.45/40.85
x = 17
Answer: The store sold 17 small cans and 34 large cans.
That took me a lot less than 23 minutes!
How did it take 23 minutes to explain this problem? Not sure this should take longer than 10 minutes even with the pre problem build up talking about all the other courses.
Add the cost of two large cans to the cost of a small can. Divide the total revenue by that number. That number is the number of small cans sold and twice that number is the number of the large cans sold. We are at six minutes of the video and I type using the hunt and peck method. The video is talking about models. Now I am getting confused and he is using variables. I'm out!
I don't think you understand the concept here, but I do understand why. This is exactly the same type of word problems my daughter was trying to resolve in her first year of collage. They throw word problems out a lot, and they insist on solving them algebraically.
@@louisd95714 'Collage?' Our class was doing these problems in 7th grade.
@@PageMarker1 This was when she first started out. It was a review of the math that the students should have been aware of and expected to know. But obviously, the word questions were much harder and more vague. I don't think I made myself clear before.
Exactly
Too much unnecessary talking
25 small and 29 large
You talk too much.
i think there might be some help here but i can never get to it! you talk so much!! i am a mum studying and i dont' have time for this. you will be loosing others because of this so i thought id say
I fell asleep 2 times before the video started, calculate that