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If
p and
q vary inversely and
p is 24 when
q is 3 , determine
q when
p is equal to 6 .
Answer:

If $p$ and $q$ vary inversely and $p$ is $24$ when $q$ is $3$ , determine $q$ when $p$ is equal to $6$ . $\newline$ Answer:

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Write and solve inverse variation equations

Full solution

Q. If

p

and

q

vary inversely and

p

is

24

when

q

is

3

, determine

q

when

p

is equal to

6

.

\newline

Answer:

Understand Relationship: Understand the relationship between $p$ and $q$ . Inverse variation means that $p$ is proportional to the reciprocal of $q$ . The formula for inverse variation is $p = \frac{k}{q}$ , 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 $p = 24$ when $q = 3$ . Substitute these values into the inverse variation formula to find $k$ . $24 = \frac{k}{3}$ Now, solve for $k$ by multiplying both sides by $3$ . $24 \times 3 = k$ $72 = k$
Write Inverse Variation Formula: Write the inverse variation formula with the found constant $k$ . Now that we know $k = 72$ , the formula becomes $p = \frac{72}{q}$ .
Find $q$ for $p = 6$ : Find $q$ when $p$ is equal to $6$ . Substitute $p = 6$ into the formula $p = \frac{72}{q}$ . $6 = \frac{72}{q}$ To solve for $q$ , multiply both sides by $q$ and then divide by $6$ . $p = 6$ $1$ $p = 6$ $2$ $p = 6$ $3$

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