Question

Eugene and Shayna are selling cheesecakes for a school fundraiser. Customers can buy French silk cheesecakes and chocolate marble cheesecakes. Eugene sold 11 French silk cheesecakes and 5 chocolate marble cheesecakes for a total of $244. Shayna sold 2 French silk cheesecakes and 8 chocolate marble cheesecakes for a total of $172. Find the cost each of one French silk cheesecake and one chocolate marble cheesecake.

Answer 1

Cost of French silk cheesecake = $11.95

Cost of chocolate marble cheesecake = $18.51

Explanation:

Let the cost of French silk cheesecake = x

and the cost of chocolate marble cheesecake = y.

From the directions given, we have the below equations in x and y

`11x+5y=224.....(1)\\\\2x+8y=172\\\\\text{Take 2 common, we get}\\\\x+4y=86.....(2)`

Multiply equation (2) with 11 and subtract from (1)

`11x+5y-11x-44y=224-946\\\\-39y=722\\\\y=18.51\\\\\text{Substitute in (2), we get}\\\\x+4(18.51)=86\\\\x=11.95`

Cost of French silk cheesecake = $11.95

Cost of chocolate marble cheesecake = $18.51