The school store sells midville high t-shirts for $12 each and midville high gym shorts for $9 a pair. one afternoon they sold a total of 53 t-shirts and pairs of shorts for a total of $570. how many t-shirts did they sell and how many pairs of shorts did they sell?

Hi there!

In order to solve this problem, we'll need to set up a system of equations. We will use the variable x  to represent the number of t-shirts, and the variable y to represent the number of shorts.

x + y = 53

This ^^ equation represents the total amount of t-shirts and shorts sold.

12x + 9y = 570

This ^^ equation represents the total amount of money that was made from selling the t-shirts and shorts.

Now, let's solve the first equation for y:

x + y = 53
y = 53 - x

Then, we'll plug in the value of y that we have just found into the second equation:

12x + 9y = 570
12x + 9(53 - x) = 570
12x + 477 - 9x = 570
3x + 477 = 570
3x = 93
x = 31

Therefore, we know that 31 t-shirts were sold at a price of $12 each. In order to solve for y, the shorts, we'll take the value of x and plug it back into the first equation.

31 + y = 53
y = 22

Therefore, we know that 31 t-shirts were sold at a price of $12 each and 22 pairs of shorts were sold at a price of $9 each. 

Hope this helps!! :)
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