Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Cumulative Review - Page 334: 31

Answer

The first number is $7$ and the second number is $11.$

Work Step by Step

Let $x$ be the second number. Then the first number is $x-4.$ The second sentence of the problem translates to \begin{array}{l}\require{cancel} 4(x-4)=2x+6 .\end{array} Using the Distributive Property and the properties of equality, the equation above is equivalent to \begin{array}{l}\require{cancel} 4(x)+4(-4)=2x+6 \\ 4x-16=2x+6 \\ 4x-2x=6+16 \\ 2x=22 \\ x=\dfrac{22}{2} \\ x=11 .\end{array} Hence, the first number is $x-4,$ equal to $7$ and the second number is $x,$ equal to $11.$
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