Official Guide Explanation:
Problem Solving #123

Background

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Solution and Metadata

Question: 123
Page: 169
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Discount >
Category 2: Arithmetic > Descriptive Statistics > Average
Category 3: Arithmetic > Percents > other

Explanation: If $207 includes a 15% gratuity, then, if x is the pre - tip price of the meal, 207 = 1.15x. Expressed differently: x = (207/(1.15)). To find the average price per person, divide that by 15, leaving you with ((x)/15) = (207/(15(1.15))). From here, it's best to estimate. 207 is a little less than 210, which is 15(14), so we can simplify to a little less than (14/(1.15)). 1.15, obviously, goes into 11.50 ten times, so it goes into 12.65 eleven times and 13.80 twelve times. Thus, (14/(1.15)) is just a little more than $12, and since we rounded up before, it's safe to assume that $12, choice (B), is the correct answer.

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