Question

Lee worked 22 hours this week and made $132. If she works 15 hours next week at the same pay rate, how much will she make?

• A. $57
• B. $90
• C. $104
• D. $112
• E. $122

Hint:

This type of problem can also be set up as a direct proportion: \( \frac{\text{Earnings}_1}{\text{Hours}_1} = \frac{\text{Earnings}_2}{\text{Hours}_2} \). Here, \( \frac{132}{22} = \frac{x}{15} \), which gives \( 6 = \frac{x}{15} \), so \( x = 90 \).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a two-step problem involving a constant rate (hourly wage). First, we must determine the rate from the given information, and then use that rate to calculate the earnings for a different number of hours.
Step 2: Key Formula or Approach:
1. Calculate the hourly pay rate: \[ \text{Rate} = \frac{\text{Total Earnings}}{\text{Hours Worked}} \] 2. Calculate the new earnings: \[ \text{New Earnings} = \text{Rate} \times \text{New Hours} \] Step 3: Detailed Explanation:
Step 1: Find the hourly pay rate.
Lee earned $132 for working 22 hours.
\[ \text{Hourly Rate} = \frac{\$132}{22 \text{ hours}} \] To simplify the division, we can note that 132 is 120 + 12, and 22 is 2 * 11. \[ \text{Hourly Rate} = \frac{132}{22} = \frac{12 \times 11}{2 \times 11} = \frac{12}{2} = \$6 \text{ per hour} \] Step 2: Calculate the earnings for 15 hours.
Next week, Lee works 15 hours at the same rate of $6 per hour.
\[ \text{New Earnings} = 15 \text{ hours} \times \$6/\text{hour} \] \[ \text{New Earnings} = \$90 \] Step 4: Final Answer:
Lee will make $90 next week. The correct option is (B).