College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 10 - Section 10.1 - Counting - 10.1 Assess Your Understanding - Page 687: 27


175 would purchase neither. 125 would only buy a car.

Work Step by Step

There are three sets of people in this exercise: $U$ is all of the people asked in the survey. $A$ is the people who would buy a car. $B$ is the people who would purchase a major appliance. $n(U)=500$ $n(A)=150$ $n(B)=200$ $n(A\cap B)=25$ Using the Counting Formula for sets: $n(A\cup B)=n(A)+n(B)-n(A\cap B)=150+200-25=325$ 325 people would purchase any of these options; therefore, $500-325=175$ would buy neither. There are 150 people who would buy a car. 25 of them would purchase a major appliance, too. Therefore, $150-25=125$ would only buy a car.
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