Question 1123162: Cameron bought 3 boxes of candy. After buying them he had $7.50 left over. His 2 friends
each bought 4 boxes of candy and had $1 left. When they walked in the store, Cameron
had the same amount of money as both of his friends combined. Write an equation to find
how much they spent on each box of candy?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let y equal the amount that cameron had to start with and the amount that his 2 friends had to start with.
let x = the price of a box of candy.
the equation for cameron is y - 3x = 7.5
the equation for his two friends is y - 8x = 2
they each bought 4 boxes of candy and had 1 dollar left.
combine what they bought and what they had left and you have 8 boxes of candy with 2 dollars left.
yout two equations that need to be solved simultaneously are:
y - 3x = 7.5
y - 8x = 2
subtract the second equiation from the first toget 5x = 5.5
divide both sides of this equation by 5 to get x = 1.1
each box of candy cost $1.10.
cameron bought 3 for a total cost of $3.30.
add that to the 7.50 that he had left, and he started with 10.80.
his two friends bought 8 for a total cost of 8.80.
add that to the 2 they had left means they started with 10.80 as well.
aolution to the problem looks good asuming the problem was interpreted correctly.
the other interpretation i had was his two friends bought 4 boxes each and had 1 dollars left in total between them.
that would change the eqaution to:
y - 3x = 7.50
y - 8x = 1
in that case, subtracting the second equation from the first yields 5x = 6.50
solve for x to get x = 6.50 / 5 = 1.30.
in that case.
y = 3 * 1.30 = 7.50 results in y = 7.50 + 3.90 = 11.40
y - 8 * 1.30 = 1 results in y = 1 + 10.40 = 11.40
so, depending on hos the problem is interpreted, the answer could be that each box cost $1.10 or each box cost $1.30.
i would tend to go with the first interpretions which resulted in a cost of $1.10 for each box of candy, but there is always that possibility that the second interpretion was the one they meant.
got to pick one, so i'd go with the first.
Answer by ikleyn(52786)  (Show Source):
You can put this solution on YOUR website! .
Let x = amount that each of Cameron's 2 friends had to start with.
The the amount which Cameron had at the start was 2x.
Let y = the price of a box of candy.
First equation is
2x - 3y = 7.50 (1) (After buying 3 boxes of candy Cameron had $7.50 left over.)
Second equation is
x - 4y = 1 (2) (His 2 friends each bought 4 boxes of candy and had $1 left.)
So, you have the system of 2 equations
2x - 3y = 7.50 (1)
x - 4y = 1 (2)
From equation (2), express x = 4y + 1 and substitute it into equation (1). You will get
2*(4y + 1) - 3y = 7.50
8y + 2 - 3y = 7.50
5y = 7.50 - 2
5y = 5.50
y =  = 1.10.
Answer. The price of one box of candy is/was $1.10.
Solved.
|
|
|
