Question 1150152: If 6 teddy bears and 5 model planes cost $162 and 5 teddy bears and 6 model planes cost $168, how much will 1 teddy bear and 1 model plane cost?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52777)   (Show Source):
You can put this solution on YOUR website! .
If 6 teddy bears and 5 model planes cost $162 and 5 teddy bears and 6 model planes cost $168,
how much will 1 teddy bear and 1 model plane cost?
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6T + 5M = 162 (1)
5T + 6M = 168 (2)
Multiply equation (1) by 5 (both sides).
Multiply equation (2) by 6 (both sides). You will get
30T + 25M = 5*162 (1')
30T + 36M = 6*168 (2')
Now subtract equation (1') from equation (2'). The terms " 30T " will cancel each other, and you will get
36M - 25M = 6*168 - 5*162
11M = 198
M =  = 18.
To find T, substitute M= 18 into equation (1). You will get
6T + 5*18 = 162
6T = 162 - 5*18 = 72
T =  = 12.
ANSWER. M = 18; T = 12.
Solved.
On the way, you learned on how the Elimination method works.
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Below is my notice, written after reading the post by @greenestanps.
@greenestamps starts his solution with this sentence
"Note that the problem does NOT ask you to find the cost of each model plane and each teddy bear.
It only asks you to find the cost of one of each."
I do not know how to decipher it "It only asks you to find the cost of one of each."
It is exactly what I did: I found the cost of each of the two models.
Probably, @greenestamps would like to say "how much 1 teddy bear and 1 model plane cost TOGETHER ?"
But the problem DOES NOT contain this word "TOGETHER".
It is his interpretation - one of the two possible interpretations.
So, it actually can be treated by any of the two ways.
Thus I solved for prices of two models separately;
@greenestamps solved for the sum of their prices.
The question is posed in such uncertain way, that ANY OF THE TWO interpretations works and is admittable.
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
Note that the problem does NOT ask you to find the cost of each model plane and each teddy bear. It only asks you to find the cost of one of each.
With the given information, that makes the solution simple.
5m + 6t = 162
6m + 5t = 168
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11m + 11t = 330
11m/11 + 11t/11 = 330/11
m + t = 30
ANSWER: The cost of one model plane and one teddy bear is $30.
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