Question

Difficulty: EasyDirect, Inverse, Joint and Partial Variation

If $y$ varies inversely as $x$ , and $y = 8$ when $x = 3$ , what is the value of $y$ when $x = 6$ ?

For inverse variation,

y = \frac{k}{x}

. Given

y = 8

when

x = 3

, the constant of variation

k = 8 \times 3 = 24

. Substituting

x = 6

gives

y = \frac{24}{6} = 4

Set up the equation for inverse variation

y = \frac{k}{x}

Inverse variation means

y

is inversely proportional to

x

with constant

k

Solve for the variation constant

k

using

y = 8

and

x = 3

k = 8 \times 3 = 24

Multiply both sides of the equation by

x

Calculate

y

when

x = 6

y = \frac{24}{6} = 4

Substitute the constant

k = 24

and

x = 6

into the inverse variation equation.

Inverse Variation

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