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An inverse variation includes the points $(25,\,2)$ 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,\,2)

and

(5,\,n)

. Find

n

.

\newline

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

\newline

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

Find $k$ : Inverse variation means $y = \frac{k}{x}$ . We got two points $(25, 2)$ and $(5, n)$ , so let's find $k$ first using the first point.
Calculate $k$ : Using the point $(25, 2)$ , we get $2 = \frac{k}{25}$ . Multiply both sides by $25$ to find $k$ .
Find $n$ : So, $2 \times 25 = k$ . That means $k = 50$ .
Substitute $k$ : Now we got $k$ , let's use the second point $(5, n)$ to find $n$ . The equation is $n = \frac{k}{5}$ .
Calculate $n$ : Substitute $k = 50$ into the equation, so $n = \frac{50}{5}$ .
Calculate $n$ : Substitute $k = 50$ into the equation, so $n = \frac{50}{5}$ .Calculate $n$ . $n = \frac{50}{5}$ gives us $n = 10$ .

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