# 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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