modeling with equations

Question

Helen earns $7.50 an hour at her job, but if she works more than 35 hours in a week, she is paid 1 1/2 times her regular salary for the overtime hours worked. One week her gross pay was $296.25. How many overtime hours did she work that week?

Answer 1

Helen earns $7.50/hr for up to 35 hours/week. Above 35 hours, she is paid 1.5 times her base pay, or $11.25/hr for each extra hour.

 

Step 1. base pay x 35 hours = base salary; $7.50/hr x 35hr = $$262.50

 

Step 2. we subtract that number from her last paycheck; $296.25 - 262.50 = $33.75

 

Step 3. we divide that number by the overtime rate to get $33.75 ÷ 11.25/hr = 3 hours

Answer 2

Assuming she worked h overtime hours that week, her gross salary would be:

 

The her total salary would be:

 

7.5 · 35 + 7.5 · 1.5 · h = 296.25.

 

Solve for h:

 

262.5 + 11.25h = 296.25

 

11.25h = 33.75

 

h = 33.75 / 11.25 = 3.

 

She worked 3 overtime hours that week.