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Earns hourly rate for 35h work and increased rate for overtime. He worked 39h and received $787.20, next worked 41h and received $844.80. hourly and overtime?

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2 Answers

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 + 6y = 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 - 8.75x

          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

let x be regular pay rate and y be overtime pay rate.

first case: worked for 39 hours, so get paid regular rate for 35 hours and overtime of 4 hours

35x + 4y = 787.20         eq. 1

second case: worked 41 hours, so get paid regular rate for 35 hours and overtime of 6 hours

35x + 6y = 844.80         eq. 2

so figure out x and y from the given equations.