Solve the Equation

Question

Jack and Tyler went shopping for summer clothes. The shirts were $12.47 each and the shorts were $17.23 per pair. Jack and Tyler spent a total of $156.21 on 11 items. How many shirts and pairs of shorts did they buy?

Answer 1

Hello, Yazmine,

We have two unknowns, the numbers of shirts (X) and shorts (Y). We need at least two equations. I'll start with an easy one. We know the total number of X and Y is 11,

X + Y = 11

We also know the total spent, so let's write an equation for the total cost by multiplying the numbers of shirts(X) and shorts(Y) by their respective prices and set that equal to the money they spent:

12.47X + 17.23Y = 156.21

Rearrange the first equation and use it in the second. X = 11 - Y

12.47(11 - Y) + 17.23Y = 156.21

137.2 - 12.47Y + 17.23Y = 156.21

4.76Y = 19.04

Y = 4 ! (I like it when the numbers are exact - it's a good feeling we're on the right track)

Since Y = 4, X must be 7 (X + Y = 11)

Check the numbers:

It works. I hope this helps, Bob