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
Sep 01, 18 04:07 PM
These heart of algebra questions will help you prepare to take the math portion of the SAT
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
Sep 01, 18 04:07 PM
These heart of algebra questions will help you prepare to take the math portion of the SAT
Our Top Pages
Formula for percentage
Compatible numbers
Basic math test
Basic math formulas
Types of angles
Math problem solver
Algebra word problems
Surface area of a cube
Finding the average
Scale drawings
Everything you need to prepare for an important exam!
K-12 tests, GED math test, basic math tests, geometry tests, algebra tests.
Real Life Math Skills
Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.