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If
p and
q vary inversely and
p is 10 when
q is 4 , determine
q when
p is equal to 20 .
Answer:

If $p$ and $q$ vary inversely and $p$ is $10$ when $q$ is $4$ , determine $q$ when $p$ is equal to $20$ . $\newline$ Answer:

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Write and solve inverse variation equations

Full solution

Q. If

p

and

q

vary inversely and

p

is

10

when

q

is

4

, determine

q

when

p

is equal to

20

.

\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 $p = 10$ when $q = 4$ . Substitute these values into the inverse variation equation $p = \frac{k}{q}$ . $10 = \frac{k}{4}$
Solve for k: Solve for k. $\newline$ Multiply both sides of the equation by $4$ to isolate k. $\newline$ $10 \times 4 = k$ $\newline$ $40 = k$
Write Inverse Variation Equation: Write the inverse variation equation with the found value of $k$ . Now that we know $k = 40$ , we can write the equation as $p = \frac{40}{q}$ .
Find $q$ for $p=20$ : Find $q$ when $p$ is equal to $20$ . Substitute $20$ for $p$ in the equation $p = \frac{40}{q}$ . $20 = \frac{40}{q}$
Solve for q: Solve for q. $\newline$ Multiply both sides of the equation by $q$ and then divide by $20$ to isolate $q$ . $\newline$ $20q = 40$ $\newline$ $q = \frac{40}{20}$ $\newline$ $q = 2$

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