Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 10 - Quadratic Equations - 10.5 - Solving Problems Using Quadratic Equations - Problem Set 10.5: 1

Answer

17,18

Work Step by Step

We take the first whole number as $x$. Since the next number will be one more than this number, the other whole number is taken as $(x+1)$. Since the product of the consecutive whole numbers is $306$, we write the following equation and solve it: $x(x+1)=306$ $x^{2}+x-306=0$ $x^{2}-17x+18x-306=0$ $x(x-17)+18(x-17)=0$ $(x-17)(x+18)=0$ $(x-17)=0$ or $(x+18)=0$ $x=17$ or $x=-18$ Disregarding the negative answer, we find that the smaller whole number is 17. This means that the larger whole number is 18.
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