Question

Ashley and Jennifer are selling cheesecakes for a school fundraiser. Customers can buy New York style cheesecakes and chocolate marble cheesecakes. Ashley sold 6 New York style cheesecakes and 14 chocolate marble cheesecakes for a total of $80. Jennifer sold 12 New York style cheesecakes and 1 chocolate marble cheesecake for a total of $52. What is the cost each of one New York style cheesecake and one chocolate marble cheesecake?

Answer 1

Cost of New York style cheesecakes = x = $4

Cost of Chocolate marble cheesecakes = y = $4

Explanation:

Ashley and Jennifer are selling cheesecakes for a school fundraiser. Let us represent:

Cost of New York style cheesecakes = x

Cost of Chocolate marble cheesecakes = y

Ashley sold 6 New York style cheesecakes and 14 chocolate marble cheesecakes for a total of $80.

6x + 14y = 80........ Equation 1

Jennifer sold 12 New York style cheesecakes and 1 chocolate marble cheesecake for a total of $52.

12x + y = 52.......... Equation 1

y = 52 - 12x

What is the cost each of one New York style cheesecake and one chocolate marble cheesecake?

Substitute 52 - 12x for y in Equation 1

6x + 14y = 80........ Equation 1

6x + 14(52 - 12x) = 80

6x + 728 - 168x = 80

6x - 168x = 80 - 728

-162x = -648

x = -648/-162

x = $4

Note: y = 52 - 12x

y = 52 - 12 ×$4

y = 52 - 48

y = $4

Cost of New York style cheesecakes = x = $4

Cost of Chocolate marble cheesecakes = y = $4