Question

Caleb and Landon work at a dry cleaners ironing shirts. Caleb can iron 30 shirts per hour, and Landon can iron 15 shirts per hour. Caleb worked 2 more hours than Landon and they ironed 330 shirts between them. Write a system of equations that could be used to determine the number of hours Caleb worked and the number of hours Landon worked. Define the variables that you use to write the system

Answer 1

The system of the equations is x - y = 2, 2x + y = 22, where x is the number of hours that Caleb worked and y is the number of hours that Landon worked

Explanation:

Assume that Caleb worked for x hours and Landon worked for y hours

∵ Caleb worked for x hours

∵ Landon worked for y hours

∵ Caleb worked 2 more hours than Landon

→ That means Caleb hours = Landon hours + 2

∴ x = y + 2

→ Subtract y from both sides

∴ x - y = 2 ⇒ (1)

∵ Caleb can iron 30 shirts per hour

∵ Landon can iron 15 shirts per hour

∵ They ironed 330 shirts between them

→ Multiply x by 30 and y by 15, then equate their sum by 330

∴ 30x + 15y = 330

→ Divide both sides by 15 to simplify the equation

∴ 2x + y = 22 ⇒ (2)

The system of the equations is x - y = 2, 2x + y = 22, where x is the number of hours that Caleb worked and y is the number of hours that Landon worked