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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?

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 man class=

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I believe the answer is 7 cakes
kanest
Set up a system of equations:

[tex]x + y = 15[/tex]
[tex]5x + 7y = 91[/tex]

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:

[tex](x + y = 15) \times -5 = (-5x - 5y = -75)[/tex]

The system should now look like this:

[tex]-5x - 5y = -75[/tex]
[tex]5x + 7y = 91[/tex]

Combine the two equations to eliminate x:

[tex]2y = 16[/tex]

Divide both sides by 2 to get y by itself:

[tex]y = 8[/tex]

There were 8 pies made.

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

[tex]x + 8 = 15[/tex]

Subtract both sides by 8 to get x by itself:

[tex]x = 7[/tex]

There were 7 cakes made.

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