Question

Amanda sold 12 pecan cheesecake and six strawberry cheesecakes for a total of $222. Calli sold two pecan cheesecake and 12 strawberry cheesecakes for total of $202. What is the cost of each type of cheesecake?

Answer 1

The cost of 1 pecan cheesecake = $11

The cost of 1 strawberry cheesecake = $15

Explanation:

Let, the cost of one pecan cheesecake = $x

And, the cost of one strawberry cheesecake = $y

So, according to the question

Amanda sells 12 pecan cheesecake and six strawberry cheesecakes for $222

⇒ 12x + 6y = $ 222

Cali sells 2 pecan cheesecake and 12 strawberry cheesecakes for $202

⇒ 2x + 12y = $ 202

Hence, the system of the equations are: 12x + 6y = $ 222

2x + 12y = $ 202

Solving these system of equations, we get

12x + 6y - 12x -72 y = 222 - 1212

or, -66 y = -990 ⇒ y = 990/66

⇒ y = 15

Putting y = 15 in 12 x+ 6 y = 222

12 x + 6(15) = 222

or, 12 x = 222 - 90 ⇒ x = 132/12 = 11

So, x = $11 , y = $15

Hence, the cost of 1 pecan cheesecake = $11

The cost of 1 strawberry cheesecake = $15