SOLUTION: Sally works at a grocery store. In one week she earned $390 for working 47 hours of which 7 hours were overtime. The next week she earn $416 for working 50 hours of which 8 hours w

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Question 139291: Sally works at a grocery store. In one week she earned $390 for working 47 hours of which 7 hours were overtime. The next week she earn $416 for working 50 hours of which 8 hours were obertime. What is Sally's hourly overtime rate in dollars per hour?
I have worked on this for 3 days now and can't get answer that works it would be great if someone could help.
Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
In one week she earned $390 for working 47 hours of which 7 hours were overtime. The next week she earn $416 for working 50 hours of which 8 hours were obertime. What is Sally's hourly overtime rate in dollars per hour?
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Let overtime rate = x; Let regular rate = y:
EQUATIONS:
7x + 40y = 390
8x + 42y = 416
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Multiply 1st equation by 8 and 2nd equation by 7 to get:
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56x + 320y = 8*390
56x + 294y = 7*416
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Subtract 2nd from 1st to get:
26y = 3120-2912
26y = 208
y = $8.00 (regular hourly rate)
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Substitute that into original 1st eq. to get:
7x + 40*8 = 390
7x = 70
x = $10.00 (overtime rate)
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Cheers,
Stan H.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
3 days is long enough...

let x="overtime rate" and let y="regular rate"

"she earned $390 for working 47 hours of which 7 hours were overtime" __ 7x+40y=390
__ subtracting 7x __ 40y=390-7x __ dividing by 40 __ y=(390-7x)/40

"she earn $416 for working 50 hours of which 8 hours were obertime" __ 8x+42y=416

substituting __ 8x+42[(390-7x)/40]=416 __ multiplying by 40 __ 320x+16380-294x=16640

subtracting 16380 __ 26x=260 __ dividing by 26 __ x=10