Question

Eli and Claire work at a dry cleaners ironing shirts. Eli can iron 15 shirts per hour,

and Claire can iron 20 shirts per hour. Eli and Claire worked a combined 17 hours
and ironed 300 shirts. Graphically solve a system of equations in order to determine
the number of hours Eli worked, x, and the number hours Claire worked, y.

Answer 1

∴ Eli worked for 8 hours and Claire worked for 9 hours

Explanation:

Let us form the two equations then graph them

∵ Eli worked for x hours

∵ Claire worked for y hours

∵ Eli and Claire worked a combined 17 hours

∴ x + y = 17 ⇒ (1)

∵ Eli can iron 15 shirts per hour

∵ Claire can iron 20 shirts per hour

∵ They ironed 300 shirts together in 17 hours

→ Multiply x by 15 and y by 20, then add the products and equate their

sum by 300

∴ 15x + 20 y = 300 ⇒ (2)

Now let us find 2 points in each equation and draw the two lines which represent the two equations

→ In equation 1, put x = 0

∵ x = 0

∵ 0 + y = 17

∴ y = 17

∴ The first point is (0, 17)

→ Put y = 0 and find x

∵ y = 0

∴ x + 0 = 17

∴ x = 17

∴ The second point is (17, 0)

→ In equation 2, put x = 0

∵ x = 0

∵ 0 + 20y = 300

∴ 20y = 300

→ Divide both sides by 20

∴ y = 15

∴ The first point is (0, 15)

→ Put y = 0 and find x

∵ y = 0

∴ 15x + 0 = 300

→ Divide both sides by 15

∴ x = 20

∴ The second point is (20, 0)

Draw the first line using points (0, 17) and (17, 0)

Draw the second line using points (0, 15) and (20, 0)

The graph is attached down

From the graph

The red line represents equation (1)

The blue line represents equation (2)

The two lines intersected at point (8, 9) which is the solution of the system of equations

∴ The solution of the two equations is (8, 9)

∴ Eli worked for 8 hours and Claire worked for 9 hours