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 * 9 = 7.5 \\ (a * 9)/(9) = (7.5)/(9) \\ a = (75)/(90) \\ a = (15)/(18)`

Now we can solve for
`q` when
`p = 24` knowing that our scalar is
`(15)/(18)\\`.

`ap = q \\ (15)/(18) * 24 = q \\ (360)/(18) = q \\ 20 = q`

Answer:

`q = 20` when
`p = 24`