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An inverse variation includes the points $(3,\,5)$ and $(1,\,n)$ . 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

(3,\,5)

and

(1,\,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, so let's use the first one to find $k$ .
Find Constant of Variation: Using the point $(3, 5)$ , we plug it into the equation: $5 = \frac{k}{3}$ .
Calculate Constant Value: Now, solve for $k$ : $k = 5 \times 3$ .
Determine Second Point: So, $k = 15$ . That's our constant of variation.
Substitute Values: Now we use $k$ to find $n$ with the second point $(1, n)$ : $n = \frac{k}{1}$ .
Final Answer: Substitute $k$ with $15$ : $n = \frac{15}{1}$ .
Final Answer: Substitute $k$ with $15$ : $n = \frac{15}{1}$ .So, $n = 15$ . That's our answer.

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