Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 9 - 9.2 - Two Variable Linear Systems - 9.2 Exercises - Page 647: 50c


$x=300; y=200$

Work Step by Step

Let $x$ and $y$ be the number of gallons of 87-octane gasoline and of 92-octane gasoline, respectively. $x+y=500 \\ 0.87 x+0.92 y=(0.89)(500)$ Therefore, the system of two equations is: $x+y=500 \\ 0.87 x+0.92 y=445$ Multiply the first equation by $-0.92$ and then add the new equation to equation $2$. $-0.92x-0.92y+0.87x+0.92 y=-460+445 $ The yields $x=300$ Substitute the value of $x$ into the first equation to get the value of $y$. $300+y=500 \implies y=200 $ Thus, $x=300; y=200$
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