Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.1 Number Theory: Prime and Composite Numbers - Exercise Set 5.1: 91

Answer

The bottles of water and cans of food should be in groups of 12.

Work Step by Step

We have 300 bottles of water and 144 cans of food. We want to sort them into equal groups of equal numbers, with only one type of item per group. To do this, we need to find the Greatest Common Divisor of 300 and 144. If we prime factor each number, we get: 300 = 2 x 2 x 3 x 5 x 5 144 = 2 x 2 x 2 x 2 x 3 x 3 The common factors are: 2 x 2 x 3 = 4 x 3 = 12 This means we can have equal sized groups if we sort into groups of 12 units each.
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