Official Guide Explanation:
Problem Solving #127




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Solution and Metadata

Question: 127
Page: 170
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Rate Problems > other
Category 2: Algebra > Equations >

Explanation: There are a couple of ways to go about this. First, the traditional way. If the packages are mailed separately, the first package costs x + 2y cents to ship, and the second costs x + 4y cents, for a total of 2x + 6y cents. If they are combined, they cost x + 7y cents to ship. The difference is (2x + 6y) - (x + 7y) = x - y. Since x is greater than y, the difference is positive, which means that shipping them separately costs more. Thus, choice (A) is correct: it's cheaper to ship them combined, and the savings is x - y cents.

Alternatively, consider the difference between the methods without doing the math. In both cases, at least one pound will be charged at the rate of x cents per pound, and at least six pounds will be charged at the rate of y cents per pound. The only difference is the charge for the remaining pound. Since y is less than x, the cheaper method is the one that results in that last pound costing y cents instead of x cents (combining them), and the difference in cost is the difference between x and y.

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