SOLUTION: A worker's period of duty increases from 56 hours to 72 hours but the wages decrease by 15%. By what percentage do the new total wages increase or decrease. ( thanks in advance)

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Question 1070857: A worker's period of duty increases from 56 hours to 72 hours but the wages decrease by 15%. By what percentage do the new total wages increase or decrease. ( thanks in advance)
Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
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A worker's period of duty increases from 56 hours to 72 hours but the wages decrease by 15%.
By what percentage do the new total wages increase or decrease. ( thanks in advance)
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You have TWO DIFFERENT kinds of wages in this problem.


One wages is "hourly wages": they decreased by 15%.


Another wages is "wages for the period of duty", and the question asks about this SECOND kind of wages.


The "old", the original "wages for the period of duty" was 56*h, where h is the old "hourly wages".

The new "wages for the period of duty" is 72*H, where H is the NEW "hourly wages".


     You are given that H = (1-0.15)h = 0.85h.


Now, new "wages for the period of duty" is W%5Bnew%5D = 72*H = 72*(0.85*h) = %2872%2F56%29%2A56%2A%280.85%2Ah%29 = %2872%2F56%29%2A0.85%2A%2856%2Ah%29 = 

= %2872%2F56%29%2A0.85.w%5Bold%5D =   (I replaced here (56*h) by w%5Bold%5D, since it is the same !)

= 1.093%2Aw%5Bold%5D.


Answer.  W%5Bnew%5D = 1.093%2Aw%5Bold%5D.

                In other words, the NEW "wages for the new period of duty" is equal to
                1.093 times the OLD "wages for the old period of duty".

Solved.