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I'm working on a problem for my accounting class and I'm trying to figure why 0.10 would become 1.1 on the other side of the equation.

Math:

Bonus = ($100,000,000 - Bonus) * 0.10

Bonus = $100,000 - 0.10 * bonus 

1.1 * Bonus = $100,000 (This is where I'm lost. Why do you add 1?)

Bonus = $90,909
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1 * Bonus = $100,000 - 0.10 * bonus -- becomes 1.1 * Bonus = $100,000 –  deinst Jul 10 '11 at 21:54

2 Answers 2

up vote 3 down vote accepted

Let $b$ be "bonus" for the sake of convenience. Then in the step which confuses you, we are adding $.1b$ to both sides of the equation. This cancels it from the right side, and the left side becomes $$b+.1b,$$ because we already have a $b$ there. So $b+.1b=1.1b$ is what you're looking for on the left.

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Let b be "bonus":

b = (100000 - b) * .1

b = 10000 - .1b

b + .1b = 10000

1.1b / 1.1 = 10000 / 1.1

b = 9,090.909090...

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