Official Guide Explanation:
Problem Solving #202




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Solution and Metadata

Question: 202
Page: 181
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Equations >
Category 2: Algebra > Simplifying Algebraic Expressions >
Category 3: Arithmetic > Percents > other

Explanation: Percents are a little tricky to work into equations. Just remember that "x percent" means ((x)/100), and you should be fine. Translating "x is m percent of y" gives you x = ((m)/100)(y) . If we call the percent we're looking for q, the question can be written y = ((q)/100)(x). To find q, rearrange the first equation to give y in terms of x, rather than the other way around:

x = ((m)/100)(y)

((x)/(y)) = ((m)/100)

(1/(y)) = ((m)/(100x))

y = ((100x)/(m)) = ((100/(m)))(x)

Thus, ((q)/100) = (100/(m)). To solve for the answer, multiply both sides by 100: q = (100/(m))(100) = ((10,000)/(m)), choice (E).

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