Official Guide Explanation:
Problem Solving #103




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Solution and Metadata

Question: 103
Page: 166
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Ratio and Proportion >
Category 2: Word Problems > Rate Problems > other
Category 3: Algebra > Linear Equations-One Unk >

Explanation: Say that there are x teachers currently at the school. Because the student - teacher ratio is currently 30:1, there are 30x students. If the student enrollment increased by 50, the number of students would be 30x + 50. If the number of teachers increased by 5, the number of teachers would be x + 5. Since, after those changes, the student - teacher ratio is 25:1, we can set up a ratio with the new numbers for students and teachers: (25/1) = ((30x + 50)/(x + 5)). The remaining steps are as follows:

25(x + 5) = 30x + 50

25x + 125 = 30x + 50

75 = 5x

x = 15

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