Question

1. russ worked a total of 135 hours during the month of july. he earned $3,600. russ earned $25 per hour each weekday that he worked. he earned $40 per hour each saturday that he worked. how many hours did he work during the weekday? how many hours did he work on the weekend?

Explanation:

Step1: Define variables

Let \( x \) be the number of weekday hours and \( y \) be the number of Saturday (weekend) hours. We know that \( x + y = 135 \) (total hours) and the total earnings equation is \( 25x + 40y = 3600 \).

Step2: Express y from the first equation

From \( x + y = 135 \), we get \( y = 135 - x \).

Step3: Substitute y into the earnings equation

Substitute \( y = 135 - x \) into \( 25x + 40y = 3600 \):
\[

$$\begin{align*} 25x + 40(135 - x) &= 3600\\ 25x + 5400 - 40x &= 3600\\ -15x &= 3600 - 5400\\ -15x &= -1800\\ x &= \frac{-1800}{-15}\\ x &= 120 \end{align*}$$

\]

Step4: Find y

Substitute \( x = 120 \) into \( y = 135 - x \):
\( y = 135 - 120 = 15 \)

Answer:

Russ worked 120 hours during the weekday and 15 hours on the weekend.