GMAT Practice Question: Last week Jack worked 70 hours and earned 1,260 dollars. If he earned his regular hourly wage...
Question
Last week Jack worked 70 hours and earned 1,260 dollars. If he earned his regular hourly wage for the first 40 hours worked, 1 \frac{1}{2} times his regular hourly wage for the next 20 hours worked, and 2 times his regular hourly wage for the remaining 10 hours worked, what was his regular hourly wage?
- 7.00 dollars per hour
- 14.00 dollars per hour
- 18.00 dollars per hour
- 22.00 dollars per hour
- 31.50 dollars per hour
Topics: word problems, linear equations, rates, translations
Solution
Step 1
We define the variable for Jack's regular hourly wage
r = \text{Jack's regular hourly wage}
Step 2
We translate \textbf{\text{"earned his regular hourly wage for the first 40 hours"}} into 40r
\text{First 40 hours} = 40r
Step 3
We translate \textbf{"1\frac{1}{2} times his regular hourly wage for the next 20 hours"} into 20 \times (1.5r)
\text{Next 20 hours} = 20 \times (1.5r) = 30r
Step 4
We translate \textbf{\text{"2 times his regular hourly wage for the remaining 10 hours"}} into 10 \times (2r)
\text{Remaining 10 hours} = 10 \times (2r) = 20r
Step 5
We set the total earnings equal to \textbf{\text{"1,260 dollars"}}
40r + 30r + 20r = 1260
Step 6
We combine like terms and solve for r
90r = 1260 r = \frac{1260}{90} = 14
Answer
Jack's regular hourly wage was 14.00, corresponding to option B.
