SOLUTION: A lifeguard earns an hourly rate for 20h work in one week and an increased rate for overtime . One week Theresa worked 24 h and received $166.40. The next week she worked 27.5h and

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Question 899751: A lifeguard earns an hourly rate for 20h work in one week and an increased rate for overtime . One week Theresa worked 24 h and received $166.40. The next week she worked 27.5h and received $200. Find her hourly rate and her overtime rate of pay.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
RT=P for rate of pay, time in hours, pay in dollars

Let r = pay rate up to 20 hours
Let u = payrate of any time amount after 20 hours

Teresa's first week:
20 hours of regular time, and 4 hours overtime time.
r%2A20%2Bu%2A4=166
20r%2B4u=166
10r%2B2u=83

Her second week:
20 hours regular time and 7.5 hours overtime.
20r%2B%287.5%29u=200
40r%2B15u=400, which although now has no fractions, still should be simplified further;
8r%2B3u=80

That forms a system of linear equations:
highlight_green%28system%2810r%2B2u=83%2C8r%2B3u=80%29%29

Choose the method you like. A good way could be, multiply first equation by 3 and second equation by 2; and eliminate u to first solve for r.
Solving from here is undone for your efforts.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A lifeguard earns an hourly rate for 20h work in one week and an increased rate for overtime . One week Theresa worked 24 h and received $166.40. The next week she worked 27.5h and received $200. Find her hourly rate and her overtime rate of pay.


Let her regular pay be r, and overtime pay, e

Then we get: 20r +   4e = 166.4 ------ eq (i)

Also,        20r + 7.5e = 200 -------- eq (ii)

Subtract eq (ii) from eq (i), or vice-versa, to obtain value of e: her overtime hourly rate. Substitute that

value for e into any of the 2 original equations to determine the value of r: her regular hourly rate.

Then do a check!! 



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