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Assume that $y$ varies inversely with $x$ . If $y = 5$ when $x = 20$ , find $y$ when $x = 4$ . $\newline$ 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 = 5

when

x = 20

, find

y

when

x = 4

.

\newline

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

\newline

y =

_____

Definition of Inverse Variation: Inverse variation means $y = \frac{k}{x}$ , where $k$ is the constant of variation.
Given Values Substitution: Given $y = 5$ when $x = 20$ , plug these values into the equation to find $k$ : $5 = \frac{k}{20}$ .
Constant Calculation: Multiply both sides by $20$ to solve for $k$ : $5 \times 20 = k$ , so $k = 100$ .
Final Inverse Variation Equation: Now we have the inverse variation equation $y = \frac{100}{x}$ .
Finding $y$ for $x=4$ : Find $y$ when $x = 4$ by substituting $x$ with $4$ : $y = \frac{100}{4}$ .
Calculation of y: Calculate y: $y = 25$ .

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