Question

If p is directly proportional to q, and p=9 when q=7.5, find q when p=24.

Answer 1

Solution and Explanation:

If $p$ and $q$ are directly proportional, then they must have a common scalar.

To find $q$ we must first find its scalar. If we let $a$ be the scalar we can form the equation, $ap = q$.

We are given the information that if $q = 7.5$ then $p = 9$. We can use that in finding the scalar.

$a \times 9 = 7.5 \\ \frac{a \times 9}{9} = \frac{7.5}{9} \\ a = \frac{75}{90} \\ a = \frac{15}{18}$

Now we can solve for $q$ when $p = 24$ knowing that our scalar is $\frac{15}{18}$.

$ap = q \\ \frac{15}{18} \times 24 = q \\ \frac{360}{18} = q \\ 20 = q$

Answer:

$q = 20$ when $p = 24$