large pies cost $7, and small pies cost $4. If 20 pies were sold for $122, how many small pies were sold

Question

how do i set this problem up?

Answer 1

Hey Koby.

 

This is a system of equations problem. You essentially have two variables you need to solve for. I'll define them below.

 

L = # of large pies sold

S = # of small pies sold

 

You have two pieces of information:

 

1) 20 total pies were sold. That means:

 

L + S = 20

 

2) Large pies are $7 each, small pies are $4 each, and you made $122 total. That means:

 

7L + 4S = 122

 

Now you have two equations, two unknowns.

 

L + S = 20

7L + 4S = 122

 

Multiply the top row by -4 and add the two equations

 

-4L - 4S = -80

7L + 4S = 122

 

3L = 42

 

L = 14

 

This means 14 large pies were sold. Since 20 pies total were sold, that means you must have sold 6 small pies.

 

Check your work:

 

Small pies are $4 a piece and you sold 6 of them, meaning you made 4*6 = $24 off small pies

Large pies are $7 a piece and you sold 14 of them, meaning you made 14*7 = $98 off large pies

 

$24 + $98 = $122, which is exactly what the problem said you made.

 

Hope this helps.