Thinking Mathematically (6th Edition)

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

Chapter 1 - Problem Solving and Critical Thinking - 1.3 Problem Solving - Exercise Set 1.3 - Page 39: 34


One way to hit a sum of $100$ is to hit $61, 19, 7$ and $13$.

Work Step by Step

It would take too long to calculate all the combinations, and the exercise only asks for one combination of four whose sum equals 100, so the proper way to solve this is by trying out different combinations with some kind of strategy, until we find one that fits the criteria. One strategy is to look for 2 numbers that make a number divisible by $10$, since such combinations are easy to spot, and then look for a combination of 2 remaining numbers that add up to the amount we need to reach 100. One of the combinations is $61$ and $19$, which add up to $61+19=80$, and then $7$ and $13$, which add up to $7+13=20$, which gives us $80+20=100$ in total. (There are more combinations that we can find with this method, including for example $51, 9, 17, 23$ and $63, 17, 7, 13$)
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