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If
p and
q vary inversely and
p is 29 when
q is 25 , determine
q when
p is equal to 145 .
Answer:

If $p$ and $q$ vary inversely and $p$ is $29$ when $q$ is $25$ , determine $q$ when $p$ is equal to $145$ . $\newline$ Answer:

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Write and solve inverse variation equations

Full solution

Q. If

p

and

q

vary inversely and

p

is

29

when

q

is

25

, determine

q

when

p

is equal to

145

.

\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 $p = 29$ when $q = 25$ . Substitute these values into the inverse variation formula to find $k$ . $29 = \frac{k}{25}$
Solve for k: Solve for k. $\newline$ Multiply both sides of the equation by $25$ to isolate $k$ . $\newline$ $29 \times 25 = k$ $\newline$ $k = 725$
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 $p = \frac{725}{q}$ .
Find $q$ for $p=145$ : Find $q$ when $p$ is equal to $145$ . Substitute $p = 145$ into the equation and solve for $q$ . $145 = \frac{725}{q}$
Solve for q: Solve for q. $\newline$ Multiply both sides by $q$ and then divide by $145$ to isolate $q$ . $\newline$ $145q = 725$ $\newline$ $q = \frac{725}{145}$ $\newline$ $q = 5$

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