Official Guide Explanation:
Problem Solving #65

Background

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Solution and Metadata

Question: 65
Page: 161
Difficulty: 4 (Moderately Easy)
Category 1: Algebra > Linear Equations-One Unk >

Explanation: We can summarize the question with an equation, where a is the number of apples and b is the number of bananas:

0.70(a) + 0.50(b) = 6.30

Generally speaking, it is impossible to solve a single equation with two variables. However, this question implies that we can solve it. Because there must be an integer number of apples and bananas, some of the mathematical possibilities (0 apples and 12.6 bananas, for instance) aren't practical.

Thus, the algebra isn't going to get us very far. Recognize that the total price of the bananas will always be either an integer dollar amount (2 bananas = 1.00) or a dollar amount plus fifty cents (5 bananas = 2.50). The total price of the apples will vary more in the cents column.

Here are the possibilities:

1 apple = 0.70

2 apples = 1.40

3 apples = 2.10

4 apples = 2.80

5 apples = 3.50

6 apples = 4.20

7 apples = 4.90

8 apples = 5.60

Since the bananas will add up to an even dollar amount or a dollar amount plus fifty cents, the apples must add up to either a dollar amount plus thirty cents or a dollar amount plus eighty cents. The only possibility is 4 apples for $2.80. That leaves $3.50 for bananas, which we can accomplish with 7 bananas. The total number, then, is 11, choice (B).

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