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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?

what is the rate for hourly and overtime

I don't know how to set up this question.

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.