Alice, who is paid time-and-a half for hours in excess of 40 hours, had gross weekly wages of $667 for 52 hours worked. what is her regular hourly rate?
Solution
Let x be her regular hourly rate
Her overtime hourly rate will be x + x/2
x + x/2 = 2x/2 + x/2 = (2x + x)/2 = 3x/2
Alice did 12 hours of overtime
Gross wage = regular wage + overtime wage (Wage equation)
Gross wage = 667
Regular wage = 40 × x
Regular wage = 40x
Overtime wage = 12 × (3x/2)
Overtime wage = (12 × 3x)/2
Overtime wage = 36x/2
Overtime wage = 18x
Replace gross wage, regular wage, and overtime wage into wage equation
667 = 40x + 18x
667 = 58x
Divide both sides by 58
667/58 = 58x/58
x = 11.5
Her regular hourly rate is 11.5
Let check it!
11.5/2 = 5.75, so overtime rate is 11.5 + 5.75 = 17.25
40 × 11.5 + 12 × 17.25 = 460 + 207 = 667
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