Find regular hourly rate

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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