Question

Find an equation of variation in which y varies directly as x and y=4 when x=24. Then find the value of y when x=120

Answer 1

Given: y varies directly as x

This can be expressed as:

$y\alpha x$

If we now introduce the constant of proportionality

$y=kx$

Next, is to find the constant of proportionality

$k=\frac{y}{x}$

since we have y=4 when x=24, then

$\begin{gathered} k=\frac{4}{24}=\frac{1}{6} \\ \\ k=\frac{1}{6} \end{gathered}$

Thus, if we plug in the value of k, we will have the equation of the variation to be:

$y=\frac{1}{6}x$

Finally, to get the value of y when x=120, we will simply put x=120 into the formula

so that

$\begin{gathered} y=\frac{1}{6}\times120=20 \\ \\ y=20 \end{gathered}$

Hence, y = 20