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 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?

GMAT Panda · Accepted Answer

Jack's regular hourly wage was 14.00, corresponding to option B. We define the variable for Jack's regular hourly wage r = Jack's regular hourly wage We translate "earned his regular hourly wage for the first 40 hours" into 40r First 40 hours = 40r We translate "11/2 times his regular hourly wage for the next 20 hours" into 20 (1.5r) Next 20 hours = 20 (1.5r) = 30r We translate "2 times his regular hourly wage for the remaining 10 hours" into 10 (2r) Remaining 10 hours = 10 (2r) = 20r We set the total earnings equal to "1,260 dollars" 40r + 30r + 20r = 1260 We combine like terms and solve for r 90r = 1260 r = 1260/90 = 14

Explanation	Calculations	Help
$We define the variable for Jack's regular hourly wage$	$r = Jack’s regular hourly wage$
$We translate "earned his regular hourly wage for the first 40 hours" into 40 r$	$First 40 hours = 40 r$
$We translate " 1 \frac{1}{2} times his regular hourly wage for the next 20 hours" into 20 \times (1.5 r)$	$Next 20 hours = 20 \times (1.5 r) = 30 r$
$We translate "2 times his regular hourly wage for the remaining 10 hours" into 10 \times (2 r)$	$Remaining 10 hours = 10 \times (2 r) = 20 r$
$We set the total earnings equal to "1,260 dollars"$	$40 r + 30 r + 20 r = 1260$
$We combine like terms and solve for r$	$90 r = 1260 r = \frac{1260}{90} = 14$

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