Question

Michael and Landon work at a dry cleaners

ironing shirts. Michael can iron 40 shirts per hour,
and Landon can iron 20 shirts per hour. Michael
and Landon worked a combined 14 hours and
ironed 360 shirts. Graphically solve a system of
equations in order to determine the number of
hours Michael worked, x, and the number hours
Landon worked, y.
Click twice to plot each line. Click a line to delete it.
20
19
19

Answer 1

x = 4, y = 10

Explanation:

Michael = 40 shirts / hr

Landon = 20 shirts / hr

Let the number of hrs Michael worked = x

Let the number of hrs Landon worked = y

If Michael and Landon worked a combined 14 hours, then x + y = 14

If Michael and Landon ironed 360 shirts, then 40x + 20y = 360

To solve this graphically

Plot the 2 equations:

x + y = 14

40x + 20y = 360

The solution is the point of intersection (4, 10), so x = 4 and y = 10.

(see attached graph)

To solve algebraically

Make y the subject of x + y = 14:

x + y = 14

⇒ y = 14 - x

Substitute y = 14 - x into 40x + 20y = 360 to find x:

40x + 20(14 - x) = 360

40x + 280 - 20x = 360

20x = 80

x = 4

Substitute found value of x into x + y = 14 to find y:

4 + y = 14

y = 14 - 4 = 10

So Michael worked 4 hours and Landon worked 10 hours.