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Question 88680: When Molly’s dot-com employer fell on bad times, she has to take a 20% cut in pay. How big a raise would she need to restore her salary to what it had been? OK; too easy. To get more than one point for this one, try give a general rule for this type of problem. If you get an x% cut in pay, what size raise do you need to restore your salary?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If you get an x% cut in pay, what size raise do you need to restore your salary?
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Let original wage be "w".
After the x% cut your wage is (100%-x%)w = (1-x/100)w = [(100-x)/100]w
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What multiple of that remaining wage will get you back to your original wage?
Let the multiple be "y".
EQUATION:
(y)[(100-x)/100]w = w
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The coefficients of w must be equal, so:
(y)[(1-(x/100)] = 1
y = 1/(1-x%)
y = 1/(1-x%)
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So if your wage is reduced 20% you would need a multiple
of 1/80% = 100/80 = 1.25
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You would need a 25% raise to get your original wage.
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Cheers,
Stan H.
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