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If
p and
q vary inversely and
p is 7 when
q is 22 , determine
q when
p is equal to 11 .
Answer:

If $p$ and $q$ vary inversely and $p$ is $7$ when $q$ is $22$ , determine $q$ when $p$ is equal to $11$ . $\newline$ Answer:

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Write and solve inverse variation equations

Full solution

Q. If

p

and

q

vary inversely and

p

is

7

when

q

is

22

, determine

q

when

p

is equal to

11

.

\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 $k$ : Use the given values to find the constant $k$ . We know that $p = 7$ when $q = 22$ . Substitute these values into the inverse variation equation $p = \frac{k}{q}$ . $7 = \frac{k}{22}$
Solve for k: Solve for k. $\newline$ Multiply both sides by $22$ to isolate $k$ . $\newline$ $7 \times 22 = k$ $\newline$ $k = 154$
Write variation equation: Write the inverse variation equation with the found value of $k$ . Now that we have $k$ , we can write the equation as $p = \frac{154}{q}$ .
Find $q$ for $p=11$ : Find $q$ when $p$ is equal to $11$ . Substitute $p = 11$ into the equation $p = \frac{154}{q}$ . $11 = \frac{154}{q}$
Solve for q: Solve for q. $\newline$ Multiply both sides by $q$ and then divide by $11$ to isolate $q$ . $\newline$ $11q = 154$ $\newline$ $q = \frac{154}{11}$ $\newline$ $q = 14$

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