Question

A corner store sells two kinds of baked goods: cakes and pies. A cake costs 5$ and a pie costs 7$. In one day, the store sold 15 baked goods for a total of 91$. How many cakes did they sell?

Answer 1

I believe the answer is 7 cakes

Answer 2

Set up a system of equations:


`x + y = 15`

`5x + 7y = 91`

x is how many cakes were made, y is how many pies were made, 5 represents the cost of each cake, and 7 represents the cost of each pie.

We'll solve the system through elimination. Multiply the entire first equation by -5:


`(x + y = 15) * -5 = (-5x - 5y = -75)`

The system should now look like this:


`-5x - 5y = -75`

`5x + 7y = 91`

Combine the two equations to eliminate x:


`2y = 16`

Divide both sides by 2 to get y by itself:


`y = 8`

There were 8 pies made.

Plug in the value for y into the original first equation:


`x + 8 = 15`

Subtract both sides by 8 to get x by itself:


`x = 7`

There were 7 cakes made.