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If
p and
q vary inversely and
p is 8 when
q is 22 , determine
q when
p is equal to 4 .
Answer:

If $p$ and $q$ vary inversely and $p$ is $8$ when $q$ is $22$ , determine $q$ when $p$ is equal to $4$ . $\newline$ Answer:

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Write and solve inverse variation equations

Full solution

Q. If

p

and

q

vary inversely and

p

is

8

when

q

is

22

, determine

q

when

p

is equal to

4

.

\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 $p = 8$ when $q = 22$ . Substitute these values into the inverse variation equation $p = \frac{k}{q}$ . $8 = \frac{k}{22}$
Solve for k: Solve for k. $\newline$ To find k, multiply both sides of the equation by $22$ . $\newline$ $8 \times 22 = k$ $\newline$ $176 = k$
Write Inverse Variation Equation: Write the inverse variation equation with the found value of $k$ . Now that we have $k = 176$ , we can write the equation as $p = \frac{176}{q}$ .
Find $q$ for $p=4$ : Find $q$ when $p$ is equal to $4$ . Substitute $p = 4$ into the equation $p = \frac{176}{q}$ . $4 = \frac{176}{q}$
Solve for q: Solve for q. $\newline$ To isolate q, multiply both sides by q and then divide by $4$ . $\newline$ $4q = 176$ $\newline$ $q = \frac{176}{4}$ $\newline$ $q = 44$

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