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An inverse variation includes the points $(25,\,3)$ and $(5,\,n)$ . Find $n$ . $\newline$ Write and solve an inverse variation equation to find the answer. $\newline$ $n = \,\_\_\_\_$

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Write and solve inverse variation equations

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Q. An inverse variation includes the points

(25,\,3)

and

(5,\,n)

. Find

n

.

\newline

Write and solve an inverse variation equation to find the answer.

\newline

n = \,\_\_\_\_

Identify Inverse Variation: Inverse variation means $y = \frac{k}{x}$ . We got two points, $(25, 3)$ and $(5, n)$ , so let's find $k$ first using the first point.
Find $k$ using $(25, 3)$ : Substitute $x = 25$ and $y = 3$ into $y = \frac{k}{x}$ to find $k$ . $\newline$ $3 = \frac{k}{25}$
Calculate $k$ : Multiply both sides by $25$ to solve for $k$ . $3 \times 25 = k$ $k = 75$
Find $n$ using $(5, n)$ : Now we know $k = 75$ , we can use the second point $(5, n)$ to find $n$ .
Find $n$ using $(5, n)$ : Now we know $k = 75$ , we can use the second point $(5, n)$ to find $n$ .Substitute $x = 5$ and $k = 75$ into $y = \frac{k}{x}$ to find $n$ . $n = \frac{75}{5}$ $n = 15$

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