Question

practice representing and solving problems with one-variable equations
javier and darius are barbers. the amount of money they earn is a combination of their hourly wage plus any tips they receive. on monday, they each worked a different number of hours, but they still earned the same amount of money. let h represent the amount of money they each earn an hour.
javier’s earnings from monday can be represented by 8h + 120.
darius’ earnings from monday can be represented by 6h + 150.
how much money do javier and darius each make an hour? how much money did javier and darius each make on monday?
use the number pad to enter your answers in the boxes.
javier and darius each make $\square$ per hour. on monday, they each made a total of $\square$

Explanation:

Step1: Set up the equation

Since their total earnings are equal, we set \(8h + 120=6h + 150\).

Step2: Solve for \(h\)

Subtract \(6h\) from both sides: \(8h - 6h+ 120=6h - 6h+ 150\), which simplifies to \(2h + 120 = 150\).
Subtract 120 from both sides: \(2h+120 - 120=150 - 120\), so \(2h = 30\).
Divide both sides by 2: \(h=\frac{30}{2}=15\).

Step3: Find total earnings

Substitute \(h = 15\) into Javier's earnings formula (\(8h + 120\)): \(8\times15+120 = 120 + 120=240\). (We could also use Darius' formula to verify: \(6\times15 + 150=90 + 150 = 240\))

Answer:

Javier and Darius each make $\boldsymbol{15}$ per hour. On Monday, they each made a total of $\boldsymbol{240}$.