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If
p and
q vary inversely and
p is 23 when
q is 27 , determine
q when
p is equal to 3 .
Answer:

If $p$ and $q$ vary inversely and $p$ is $23$ when $q$ is $27$ , 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

23

when

q

is

27

, 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 $p = 23$ when $q = 27$ . Substitute these values into the inverse variation equation $p = \frac{k}{q}$ . $23 = \frac{k}{27}$
Solve for k: Solve for k. $\newline$ Multiply both sides by $27$ to isolate $k$ . $\newline$ $23 \times 27 = k$ $\newline$ $k = 621$
Write Inverse Variation Equation: Write the inverse variation equation with the found value of $k$ . Now that we have $k$ , we can write the equation as $p = \frac{621}{q}$ .
Find $q$ for $p=3$ : Find $q$ when $p$ is equal to $3$ . Substitute $p = 3$ into the equation $p = \frac{621}{q}$ . $3 = \frac{621}{q}$
Solve for q: Solve for q. $\newline$ Multiply both sides by $q$ and then divide by $3$ to isolate $q$ . $\newline$ $3q = 621$ $\newline$ $q = \frac{621}{3}$ $\newline$ $q = 207$

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