Judy worked 8 hours and Ben worked 10 hours. Their combines pay was 80 dollars. When Judy worked 9 hours and Ben worked 5 hours, their combined pay was $65. Find the hourly rate of pay for each person

Answer 1

Let \( x \) be Judy's hourly rate and \( y \) be Ben's hourly rate.

From the information given, we can set up the following equations based on their hours worked and their combined pay:

1. For the first situation (Judy worked 8 hours and Ben worked 10 hours), we have: \[ 8x + 10y = 80 \]

2. For the second situation (Judy worked 9 hours and Ben worked 5 hours), we have: \[ 9x + 5y = 65 \]

Now we have the system of equations:

\[ \begin{align*}

1. & \quad 8x + 10y = 80 \quad \text{(1)} \
2. & \quad 9x + 5y = 65 \quad \text{(2)} \ \end{align*} \]

To solve these equations, we can first simplify equation (1) by dividing everything by 2:

\[ 4x + 5y = 40 \quad \text{(3)} \]

Now we have:

\[ \begin{align*} 3) & \quad 4x + 5y = 40 \ 2) & \quad 9x + 5y = 65 \ \end{align*} \]

Next, we'll eliminate \( y \) by subtracting equation (3) from equation (2):

\[ (9x + 5y) - (4x + 5y) = 65 - 40 \] \[ 5x = 25 \] \[ x = 5 \]

Now that we have \( x \), we can substitute \( x = 5 \) back into equation (3) to find \( y \):

\[ 4(5) + 5y = 40 \] \[ 20 + 5y = 40 \] \[ 5y = 20 \] \[ y = 4 \]

Thus, Judy's hourly rate is \( \boxed{5} \) dollars per hour, and Ben's hourly rate is \( \boxed{4} \) dollars per hour.