Kayla and Joe's Cheese cake fundraiser

Question

Kayla and Joe are selling cheesecakes for a school fundraiser. Customers can buy New York style cheesecake and strawberry cheesecakes. Kayla sold 12 New York style cheesecakes and 9 strawberry cheesecakes for a total of $192. Joe sold 6 New York style cheesecakes and 14 strawberry cheesecakes for a total of $210. what is the cost each of one New York style cheesecake and one strawberry cheesecake?

Answer 1

Hi Nicholas,

This is another system of equations problem. New York Cheesecakes would represent one variable (x) and the Strawberry Cheesecakes would represent the other variable (y). The two equations are what Joe and Kayla sold:

Kayla: 12x + 9y = 192

Joe: 6x + 14y = 210

Elimination would be the easiest method to solve this problem by multiplying Joe's equation by 2 so that we are comparing the same amount of New York Cheesecakes (x):

Kayla: 12x + 9y = 192

Joe: 12x + 28y = 420

Then we can combine equations using subtraction to eliminate the x variable:

-19y = -228

Then we would divide by -19 to solve the cost of a Strawberry Cheesecake (y):

y = $12 (Since a negative divided by a negative equals a positive number)

Now that we know the cost of a strawberry cheesecake, we plug that price in to one equation to solve for the cost of a New York Cheesecake (x):

12x + 9(12) = 192

12x + 108 = 192

-108 -108

12x = 84

Then we would divide by 12 to get the cost of x, one New York cheesecake: x = $7

This means that a New York Cheesecake is $7 and a Strawberry Cheesecake is $12