Understanding Rational Expressions - High School Math

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Question

Solve:

If varies directly as , and when , find when .

Answer

The formula for a direct variation is:

$\frac{x_1}{x_2}=\frac{y_1}{y_2}$

Plugging in our values, we get:

$\frac{7}{x}=\frac{21}{-5}$

$x= \frac{-5}{3}$

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Question

If two boxes have the same depth and capacity, the length is inversely proportional to the width. One box is $60\ cm$ long and $40\ cm$ wide. A second box (same depth and capacity) is $5\ cm$ long. How wide is it?

Answer

The formula for an indirect variation is:

$\frac{x_1}{x_2}=\frac{y_2}{y_1}$

Plugging in our values, we get:

$\frac{60\ cm}{5\ cm}=\frac{y}{40\ cm}$

$5y=2400\ cm$

$y=480\ cm$

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