Compute hourly wage

Question

Leigh is paid time-and-a-half for hours worked in excess of 40 hrs and double-time for hours worked on Sunday. If Leigh had gross weekly wages of 798$ for working 50 hrs, 4 of which were on Sunday. What is her regular hourly rate?

Answer 1

This problem could be solved in two different ways.

 

Method 1 (Standard Method): Setting up an equation with the unknown variable as the regular hourly rate:

 

Let x denotes the regular hourly rate, according to the description of the problem, for hours worked in excess of 40 hrs (not Sunday) the hourly rate is 1.5x; for hours worked on Sunday the hourly rate is 2x.

 

Leigh worked 50 hrs, among which 4 of them are on Sunday, which are paid with 2x per hour. We deduce that 50 - 40 - 4 = 6 hours are paid with 1.5x per hour.

 

We have 40*x + 6*1.5x+4*2x = $798, i.e. 57x = $798. We can find out that x = $798/57 = $14.

 

So the regular hourly rate is $14/hr.

 

Method 2 (Simpler but require more thought):

 

Instead of considering double rate on Sunday, we can see thing in another angle: working one hour on Sunday is as working 2 hours on a weekday that receives regular hourly pay.

 

Hence, since Leigh works 6 hours beyond 40 hours threshold and 4 hours on Sunday, it is as if he has worked for 40 + 1.5*6 + 2*4 = 57 hours with a regular hourly pay.

 

Since he got paid $798 in total, so the regular hourly rate should be $798/57hr = $14/hr.

 

 

Answer 2

Daisy, to answer this question you need to write and solve an equation.

 

First, let's define our variable.  Let x = Leigh's regular hourly rate (what we are trying to find).  So:

 

x = regular hourly rate

1.5x = rate for hours in excess of 40

2x = rate for Sunday hours

 

The problem tells us she worked 50 hours, 4 of which were on Sunday.  Therefore she must have worked (50 minus 4 minus 40 =) 6 hours at the 1.5x rate.

 

Let's put it all together in an equation, then solve it:

 

40x  +  6(1.5x)  +  4(2x)  = 798

 

 40x     +  9x        +  8x    = 798

 

                 57x                =  798

 

              57x/57              =  798/57

 

                   x                  =  14

 

Her regular hourly rate is $14.  Ok?