Question

Suppose p varies directly with d, and p = 3 when d = 5. What is the value of d when p = 12?

Answer 1

So we need to find the constant here...

Direct variation would be

\[\large y = kx\]
or for your variables
\[\large p = kd\]

So what we do is plug in the 2 numbers we are given...and solve for 'k'

\[\large 3= 5k\]
\[\large k = \frac{3}{5}\]

Now that we know that...we can solve the last part...when 'p' = 12...what is D?

Well

\[\large p = \frac{3}{5}d\]
\[\large 12 = \frac{3}{5}d\]
\[\large d = 12 \times \frac{5}{3}\]