Answer: The number of boxes of cookies that makes the costs equal is 3
Step-by-step explanation:
A store charges $13.75 for 5 boxes of cookies. This means the charge per cookie is 13.75/5 = $2.75
Therefore, for x cookies, the store charges 2.75 × x = $2.75x
A second store charges $9.00 for 4 boxes of cookies. This means the charge per cookie is 9/4 = $2.25
Therefore, for x cookies, the store charges 2.25 × x = $2.25x but you have to buy a gallon of milk for $1.50 to get that deal.
This means that at the second store, the charge for x cookies will be
2.25x + 1.50. Therefore, the cost model equations for both boxes are
Cost of x boxes cookies at first store, C(x)= $2.75x
Cost of x boxes of cookies at second store, C(x) = 2.25x + 1.50
To find number of boxes of cookies that make both costs equal,
2.75x = 2.25x + 1.50
2.75x - 2.25x = 1.50
0.5x = 1.5
x = 1.5/0.5 = 3
