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An inverse variation includes the points $(8,\,3)$ 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

(8,\,3)

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. $\newline$ Inverse variation: $y = \frac{k}{x}$ where $k$ is the constant of variation.
Find constant of variation: We are given the points $(8, 3)$ and $(4, n)$ . Use the first point $(8, 3)$ to find the constant of variation $k$ . Substitute $8$ for $x$ and $3$ for $y$ in $y = \frac{k}{x}$ . $3 = \frac{k}{8}$
Solve for $k$ : Solve the equation to find the value of $k$ . To isolate $k$ , multiply both sides by $8$ . $3 \times 8 = \left(\frac{k}{8}\right) \times 8$ $24 = k$
Write inverse variation equation: Now that we have the constant of variation $k = 24$ , we can write the inverse variation equation. $y = \frac{24}{x}$
Find value of $n$ : Use the second point $(4, n)$ to find the value of $n$ . $\newline$ Substitute $4$ for $x$ in $y = \frac{24}{x}$ . $\newline$ $n = \frac{24}{4}$ $\newline$ $n = 6$

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