Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 6 - Section 6.6 - Variation - 6.6 Exercises - Page 418: 36

Answer

$y=35$

Work Step by Step

Recall: If $y$ varies directly as $x$ then, $y=kx$ where $k$ is the constant of variation. Since $x=10$ when $y=7$, then: \begin{align*} y&=kx\\\\ 7&=k(10)\\\\ \frac{7}{10}&=\frac{k(10)}{10}\\\\ \frac{7}{10}&=k \end{align*} Thus, the direct variation's equation is: $$y=\frac{7}{10}x$$ To find the value of $y$ when $x=50$, substitute these values into the equation above to obtain: \begin{align*} y&=\frac{7}{10}x\\\\ y&=\frac{7}{10}(50)\\\\ y&=7(5)\\\\ y&=35 \end{align*}
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