Question 496124: Butch and Peggy need some cardboard boxes. They can buy 10 small and 20 large boxes for $65, or 6 small and 10 large for $34. Find the cost of each size of box.
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! This is pretty straightforward. Whenever you see problems like this, two equations with two unknowns, the method is to state the problem in terms of only one unknown, solve for that, then plug that answer back into one of the original questions to solve for the other unknown. Then, of course, plug both solved values back into both equations to check your work. Always check your work (because you could have the method right but make a silly arithmetic error and then doubt your solution).
...
Lets let L = the price of large boxes and S = the price of small boxes. We were given:
...
10S + 20L = 65
6S + 10L = 34
...
In algebra, we have a lot of latitude to change these equations around to make them easier to work with, as long as when we make a change on one side of the equation we make the same change to the other.
...
An easy way to reduce one of these equations to dealing with only one unknown is to find a way to cancel out one of the terms. If the 2nd equation with the 10L term in it was 20L, we could (and will) subtract one entire equation from the other.
...
6S + 10L = 34 is functionally the same as:
12S + 20L = 68
...
So, if we take our modified 2nd equation and subtract the 1st equation, the 20L's will cancel out, leaving us one equation with one unknown, which we can easily solve:
...
(12S + 20L = 68)
- (10S + 20L = 65)
-----------------
2S + 0L = 3
...
But we only want 1S, so we divide both sides by 2:
...
S = 1.5
...
Going back into either of our 1st two equations with S = 1.5, we now have another case of 1 equation with 1 unknown, which we can easily solve:
...
10(1.5) + 20L = 65
15 + 20L = 65
...
Subtract 15 from both sides so we can have the L on one side of the equality:
...
20L = 65 - 15
20L = 50
...
divide by 20 to get:
...
L = 2.5
...
Going back to both original equations:
...
10(1.5) + 20(2.5) = 65
15 + 50 = 65
65 = 65 (true)
...
6(1.5) + 10(2.5) = 34
9 + 25 = 34
34 = 34 (true)
...
Our work checks and our solution is valid. Small boxes cost $1.50 ea and large boxes cost $2.50 ea.
...
cheers,
Lee
|
|
|
