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Assume that $y$ varies inversely with $x$ . If $y = 2$ when $x = 20$ , find $y$ when $x = 5$ . $\newline$ 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. Assume that

y

varies inversely with

x

. If

y = 2

when

x = 20

, find

y

when

x = 5

.

\newline

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

\newline

y =

_____

Identify Inverse Variation: Inverse variation means $y = \frac{k}{x}$ . We need to find $k$ using the given values.
Find $k$ using given values: Substitute $y = 2$ and $x = 20$ into $y = \frac{k}{x}$ to find $k$ . So, $2 = \frac{k}{20}$ .
Substitute values into equation: Multiply both sides by $20$ to solve for $k$ . $2 \times 20 = k$ , which means $k = 40$ .
Calculate $k$ : Now we have $k$ , so the equation is $y = \frac{40}{x}$ . Let's find $y$ when $x = 5$ .
Find $y$ when $x = 5$ : Substitute $x = 5$ into $y = \frac{40}{x}$ . So, $y = \frac{40}{5}$ .
Find $y$ when $x = 5$ : Substitute $x = 5$ into $y = \frac{40}{x}$ . So, $y = \frac{40}{5}$ .Calculate $y$ . $y = \frac{40}{5} = 8$ .

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