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An inverse variation includes the points $(16,\,2)$ and $(4,\,n)$ . 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

Full solution

Q. An inverse variation includes the points

(16,\,2)

and

(4,\,n)

. Find

n

.

\newline

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

\newline

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

Identify general form: Given that there is an inverse variation between two variables. $\newline$ Identify the general form of inverse variation. $\newline$ In inverse variation, one variable is directly proportional to the reciprocal of the other. $\newline$ Inverse variation formula: $y = \frac{k}{x}$ where $k$ is the constant of variation.
Find constant of variation: We are given the points $(16, 2)$ which means when $x = 16$ , $y = 2$ . Use this information to find the constant of variation $k$ . Substitute $16$ for $x$ and $2$ for $y$ in the formula $y = k / x$ . $2 = k / 16$
Write inverse variation equation: Solve for $k$ by multiplying both sides of the equation by $16$ . $2 \times 16 = k$ $32 = k$ Now we have found the constant of variation $k = 32$ .
Substitute values to find $n$ : Use the constant of variation $k = 32$ to write the inverse variation equation. $\newline$ The equation is $y = \frac{32}{x}$ .
Calculate value of $\newline$ : We are given another point ( $4$ , n) which means when x = $4$ , y = n. $\newline$ Substitute k = $32$ and x = $4$ into the inverse variation equation to find n. $\newline$ n = $32$ / $4$
Calculate value of n: We are given another point $(4, n)$ which means when $x = 4$ , $y = n$ . $\newline$ Substitute $k = 32$ and $x = 4$ into the inverse variation equation to find $n$ . $\newline$ $n = \frac{32}{4}$ Calculate the value of $n$ . $\newline$ $n = \frac{32}{4}$ $\newline$ $n = 8$ $\newline$ We have found the value of $n$ .

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