what is the rate for hourly and overtime
I don't know how to set up this question.
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.