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If
p and
q vary inversely and
p is 9 when
q is 13 , determine
q when
p is equal to 39 .
Answer:

If $p$ and $q$ vary inversely and $p$ is $9$ when $q$ is $13$ , determine $q$ when $p$ is equal to $39$ . $\newline$ Answer:

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Write and solve inverse variation equations

Full solution

Q. If

p

and

q

vary inversely and

p

is

9

when

q

is

13

, determine

q

when

p

is equal to

39

.

\newline

Answer:

Identify general form: Given that $p$ and $q$ vary inversely. $\newline$ Identify the general form of inverse variation. $\newline$ Inverse variation: $p = \frac{k}{q}$
Substitute values to find constant: We know that $p = 9$ when $q = 13$ . Substitute $9$ for $p$ and $13$ for $q$ in $p = \frac{k}{q}$ to find the constant of variation $k$ . $9 = \frac{k}{13}$
Solve for constant: Solve the equation to find the value of $k$ . Multiply both sides by $13$ to isolate $k$ . $9 \times 13 = k$ $117 = k$
Write inverse variation equation: Write the inverse variation equation using the value of $k$ . Substitute $k = 117$ into $p = \frac{k}{q}$ . $p = \frac{117}{q}$
Find $q$ when $p=39$ : Find $q$ when $p = 39$ . $\newline$ Substitute $39$ for $p$ in $p = \frac{117}{q}$ . $\newline$ $39 = \frac{117}{q}$
Solve for q: Solve the equation to find the value of $q$ . Multiply both sides by $q$ and then divide by $39$ to isolate $q$ . $39q = 117$ $q = \frac{117}{39}$ $q = 3$

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