Question

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?

a. 33 T-shirts and 20 pairs of shorts
b. 22 T-shirts and 31 pairs of shorts
c. 31 T-shirts and 22 pairs of shorts
d. 34 T-shirts and 18 pairs of shorts

Answer 1

To solve this problem, we can set up a system of equations. Let x represent the number of T-shirts sold and y represent the number of pairs of shorts sold. Using the given information and equations, we can solve for x and y to find that they sold 31 T-shirts and 22 pairs of shorts.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let x represent the number of T-shirts sold and y represent the number of pairs of shorts sold. We are given two pieces of information: the total number of T-shirts sold and pairs of shorts sold is 53, and the total amount of money earned is $570.

We can write the following equations:

x + y = 53 (equation 1)

12x + 9y = 570 (equation 2)

From equation 1, we can solve for y:

y = 53 - x

Substitute this into equation 2:

12x + 9(53 - x) = 570

Distribute and simplify:

12x + 477 - 9x = 570

Combine like terms:

3x + 477 = 570

Subtract 477 from both sides:

3x = 93

Divide both sides by 3:

x = 31

Now we can substitute this value back into equation 1 to find y:

31 + y = 53

Subtract 31 from both sides:

y = 22

Therefore, they sold 31 T-shirts and 22 pairs of shorts.