Tamara J. answered • 05/14/13

Math Tutoring - Algebra and Calculus (all levels)

Given: earns regular hourly rate for 35 hours and earns overtime hourly rate for working extra hours

received a total of $787.20 for working 39 hours

==> earns regular rate for 35 hours and overtime rate for 4 hours

received a total of $844.80 for working 41 hours

==> earns regular rate for 35 hours and overtime rate for 6 hours

Let 'x' represent the regular rate earned per hour and 'y' represent the overtime rate earned per hour. That is,

x = regular rate per hour

y = overtime rate per hour

With this, we arrive at the following system of linear equations:

** (1) 35x + 4y = 787.20**

** (2) 35x + 6y = 844.20**

To solve by substitution, solve one of the above equations for one of the variables (either x or y) then substitute this into the other equation. For instance, let's solve equation (1) for y:

(1) 35x + 4y = 787.20

subtract 35x from both sides

4y = 787.20 - 35x

divide both sides by 4

4y/4 = 787.20/4 - 35x/4

**y = 196.80 - 8.75x**

(2) 35x + 6**y** = 844.80

35x + 6(**196.80 - 8.75x**) = 844.80

distribute the 6 into each term inside the parenthesis

35x + 1180.80 - 52.50x = 844.80

combine like terms

-17.50x + 1180.80 = 844.80

subtract 1180.80 from both sides

-17.50x = -336

divide both sides by -17.50

** x = 19.20**

Now that we've solved for x, solve for y by substituting the value found for x into the equation we determined for y:

y = 196.80 - 8.75**x**

y = 196.80 - 8.75(**19.20**)

y = 196.80 - 168

**y = 28.80**

Thus,

**x = regular hourly rate** ==> **$19.20/hr**

**y = overtime hourly rate** ==> ** $28.80/hr**