Question

If y varies directly as x and y = 48 when x = 15, find x when y = 16

Answer 1

As y varies directly as x, we have a linear relation for x and y that goes through the origin (the point (0, 0) belongs to the line).

Other point that belongs to the linear relation is (x=15; y=48).

We have the relation:

`y=mx+b`

b=0, as y varies directly as x.

Using the point (15, 48) we have:

`\begin{gathered} 48=m\cdot15+0 \\ m=(48)/(15) \\ m=3.2 \end{gathered}`

Then, the equation that relates y to x is:

`y=3.2x`

When y=16, this corresponds to an x value of:

`\begin{gathered} y=16=3.2x \\ x=(16)/(3.2)=5 \end{gathered}`

When y=16, x=5.