Question

Jillian is selling boxes of cookies to raise money for her basketball team. the 10 oz. box costs $3.50, while the 16 oz. box costs $5.00. at the end of one week, she collected $97.50, selling a total of 24 boxes. the system of equations that models her sales is below.

x y= 24

3.50x 5.00y = 97.50

solve the system of equations. how many 10 oz. boxes were sold?

6
9
12
15

Answer 1

x + y = 24...y = 24 - x
3.50x + 5.00y = 97.50

3.50x + 5(24 - x) = 97.50
3.50x + 120 - 5x = 97.50
3.50x - 5x = 97.50 - 120
-1.5x = -22.50
x = -22.50/-1.5
x = 15....there were 15 ten oz boxes (x) sold

Answer 2

15

Explanation:

If 10 oz. box costs $3.50 and a 16 oz. box costs $5.00 and she collected $97.50 we can represent an expression that relates for how many money Jillian made:

`3.5*x+5*y=97.50` (1)

where x is the number of 10 oz. boxes and y is the number of 16 oz. boxes.

She sold 24 boxes therefore:

`x+y=24` (2)

We can right equation in terms of y and substitute it into equation 1:

`y=24-x` (2)

`3.5*x+5*(24-x)=97.50`

Solve for x:

`x=15`

Jillian sold 15 10oz. boxes