Question

If y varies directly as x and y=80 when x=32 find x when y = 100.

Answer 1

Since y varies directly as x, we have that this expression is true:

$y=kx$

Now, we are given the information that y=80 when x=32, then we can find k easily like this:

$\begin{gathered} y=kx \\ \Rightarrow80=k\cdot(32) \\ \Rightarrow k=\frac{80}{32}=\frac{5}{2} \\ k=\frac{5}{2} \end{gathered}$

Finally, to find x when y=100, we substitute each value and solve for x the resulting expression:

$\begin{gathered} y=kx \\ \Rightarrow100=\frac{5}{2}\cdot x \\ \Rightarrow100\cdot2=5x \\ \Rightarrow200=5x \\ \Rightarrow x=\frac{200}{5}=40 \\ x=40 \end{gathered}$

Therefore, x=40 when y=100