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If $y$ varies inversely with $x$ and $y = 5$ when $x = 8$ , find $y$ when $x = 2$ . $\newline$ Write and solve an inverse variation equation to find the answer. $\newline$ $y =$ _____

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Write and solve inverse variation equations

Full solution

Q. If

y

varies inversely with

x

and

y = 5

when

x = 8

, find

y

when

x = 2

.

\newline

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

\newline

y =

_____

Define Inverse Variation: Inverse variation means $y = \frac{k}{x}$ . We need to find $k$ using the given values $y = 5$ and $x = 8$ .
Substitute Values: Substitute $y = 5$ and $x = 8$ into the equation to get $5 = \frac{k}{8}$ .
Solve for Constant: Multiply both sides by $8$ to solve for $k$ : $5 \times 8 = k$ .
Write Equation with Constant: $k = 40$ . Now we have the constant of variation.
Find $y$ for $x=2$ : Write the inverse variation equation with $k$ : $y = \frac{40}{x}$ .
Find $y$ for $x=2$ : Write the inverse variation equation with $k$ : $y = \frac{40}{x}$ .Find $y$ when $x = 2$ by substituting $x = 2$ into $y = \frac{40}{x}$ .
Find $y$ for $x=2$ : Write the inverse variation equation with $k$ : $y = \frac{40}{x}$ .Find $y$ when $x = 2$ by substituting $x = 2$ into $y = \frac{40}{x}$ . $y = \frac{40}{2}$ .
Find $y$ for $x=2$ : Write the inverse variation equation with $k$ : $y = \frac{40}{x}$ .Find $y$ when $x = 2$ by substituting $x = 2$ into $y = \frac{40}{x}$ . $y = \frac{40}{2}$ . $y = 20$ . So when $x = 2$ , $y = 20$ .

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