Tricia?, who is paid? time-and-a-half for hours worked in excess of 40? hours, had gross weekly wages of $ 416 for 56 hours worked. What is her

Question

Tricia?, who is paid? time-and-a-half for hours worked in excess of 40? hours, had gross weekly wages of $ 416 for 56 hours worked. What is her regular hourly? rate?

Answer 1

In this problem, pay (let it be: y) is a function of hours worked (let it be x):  y=f(x) means pay=f(hours).

We are given both the pay and the hours, and asked to find the regular hourly rate.  So, we start by assigning a variable, R, to the regular hourly rate.  This means that 1.5*R is the overtime rate ("time-and-a-half).  The hours worked at the regular rate is 40 (meaning that we are writing a formula that only works for hours>=40) is 40.  The hours worked at the time-and-a-half rate is 56-40=16.  So, write the function and solve for R:

 

   pay = f(hours)

   $416 = 40*R + 16*1.5*R

    416 = 64R                  (collect terms)

    $6.50 = R

 

Checking (very important):

  Is 416 = 40*(6.5) + 16*1.5*(6.5)   ?

      416 = 416  ?   yes.