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Karl was attempting to calculate economic figures. He found the following equation to be true:\[fp-w=10000\]If $f=5$ and $w=5+125i$, what is $p$?

 May 11, 2019
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Solve for p:
(-125 i - 5) + 5 p = 10000

Add 5 + 125 i to both sides:


5 p + ((-125 i - 5) + 125 i + 5) = 125 i + 5 + 10000

(-125 i - 5) + (125 i + 5) = 0:


5 p = 10000 + 5 + 125 i

10000 + 5 + 125 i = (10000 + 5) + 125 i = 10005 + 125 i:


5 p = 125 i + 10005

Divide both sides of 5 p = 125 i + 10005 by 5:


(5 p)/5 = (125 i + 10005)/5
p = (125 i + 10005)/5

 May 11, 2019

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