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If
p and
q vary inversely and
p is 25 when
q is 28 , determine
q when
p is equal to 70 .
Answer:

If $p$ and $q$ vary inversely and $p$ is $25$ when $q$ is $28$ , determine $q$ when $p$ is equal to $70$ . $\newline$ 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

28

, determine

q

when

p

is equal to

70

.

\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 $q = 28$ . Substitute these values into the inverse variation formula to find $k$ . $25 = \frac{k}{28}$ Now, solve for $k$ by multiplying both sides by $28$ . $25 \times 28 = k$ $k = 700$
Write Inverse Variation Equation: Write the inverse variation equation with the found constant $k$ . Now that we have found $k$ to be $700$ , we can write the equation as $p = \frac{700}{q}$ .
Find $q$ for $p=70$ : Find $q$ when $p$ is equal to $70$ using the inverse variation equation. $\newline$ Substitute $p = 70$ into the equation $p = \frac{700}{q}$ . $\newline$ $70 = \frac{700}{q}$ $\newline$ To find $q$ , multiply both sides by $q$ and then divide by $70$ . $\newline$ $p=70$ $1$ $\newline$ $p=70$ $2$ $\newline$ $p=70$ $3$

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