Intermediate Algebra (6th Edition)

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

Chapter 4 - Section 4.2 - Solving Systems of Linear Equations in Three Variables - Exercise Set - Page 220: 30

Answer

Larger number is $9$. Smaller number is $4$.

Work Step by Step

Let Larger number be $x$ and Smaller number be $y$. Difference of two numbers is $5$ $x - y = 5$ Equation$(1)$ Twice the smaller number added to five times larger number is $53$. $2y + 5x = 53$ $5x + 2y = 53$ Equation $(2)$ From Equation $(1)$ we get, $x = y +5$ Substituting $x$ in Equation $(2)$ $5(y+5) + 2y = 53$ $5y+25 + 2y = 53$ $7y +25 = 53$ $7y = 53-25$ $7y = 28$ $y = 4$ Substituting $y$ value in Equation $(1)$, $x - y = 5$ $x - 4 = 5$ $x = 5+4$ $x = 9$ Larger number is $9$. Smaller number is $4$.
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