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If
p and
q vary inversely and
p is 6 when
q is 2 , determine
q when
p is equal to 3 .
Answer:

If $p$ and $q$ vary inversely and $p$ is $6$ when $q$ is $2$ , determine $q$ when $p$ is equal to $3$ . $\newline$ Answer:

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Write and solve inverse variation equations

Full solution

Q. If

p

and

q

vary inversely and

p

is

6

when

q

is

2

, determine

q

when

p

is equal to

3

.

\newline

Answer:

Understand relationship: Understand the relationship between $p$ and $q$ . Since $p$ and $q$ vary inversely, we can write the relationship as $p = \frac{k}{q}$ , where $k$ is the constant of variation.
Find constant of variation: Use the given values to find the constant of variation $k$ . We know that $p = 6$ when $q = 2$ . Substitute these values into the inverse variation equation $p = \frac{k}{q}$ . $6 = \frac{k}{2}$
Solve for k: Solve for k. $\newline$ To find k, multiply both sides of the equation by $2$ . $\newline$ $6 \times 2 = k$ $\newline$ $12 = k$
Write inverse variation equation: Write the inverse variation equation with the found value of $k$ . Now that we know $k = 12$ , we can write the equation as $p = \frac{12}{q}$ .
Find $q$ for $p=3$ : Find $q$ when $p$ is equal to $3$ . Substitute $p = 3$ into the equation $p = \frac{12}{q}$ . $3 = \frac{12}{q}$
Solve for q: Solve for q. $\newline$ To isolate q, multiply both sides by q and then divide by $3$ . $\newline$ $3q = 12$ $\newline$ $q = \frac{12}{3}$ $\newline$ $q = 4$

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