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If
p and
q vary inversely and
p is 25 when
q is 29 , determine
q when
p is equal to 5 .
Answer:

If $p$ and $q$ vary inversely and $p$ is $25$ when $q$ is $29$ , determine $q$ when $p$ is equal to $5$ . $\newline$ Answer:

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Write and solve inverse variation equations

Full solution

Q. If

p

and

q

vary inversely and

p

is

25

when

q

is

29

, determine

q

when

p

is equal to

5

.

\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 $p = 25$ when $q = 29$ . Substitute these values into the inverse variation equation $p = \frac{k}{q}$ . $25 = \frac{k}{29}$
Solve for k: Solve for k. $\newline$ To find k, multiply both sides of the equation by $29$ . $\newline$ $25 \times 29 = k$ $\newline$ $k = 725$
Write Inverse Variation Equation: Write the inverse variation equation with the found value of $k$ . Now that we have $k$ , the equation becomes $p = \frac{725}{q}$ .
Find $q$ for $p=5$ : Find $q$ when $p$ is equal to $5$ . $\newline$ Substitute $p = 5$ into the equation $p = \frac{725}{q}$ . $\newline$ $5 = \frac{725}{q}$
Find $q$ for $p=5$ : Find $q$ when $p$ is equal to $5$ . Substitute $p = 5$ into the equation $p = \frac{725}{q}$ . $5 = \frac{725}{q}$ Solve for $q$ . To isolate $q$ , multiply both sides by $q$ and then divide by $5$ . $p=5$ $2$ $p=5$ $3$ $p=5$ $4$

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