Question

Y varies directly as x. If x=6 then y=3. Find y when x=15.

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given variation

$\begin{gathered} Direct\text{ }Variation \\ y\propto x \end{gathered}$

STEP 2: Find the constant of variation

$\begin{gathered} If\text{ }y\propto x \\ Then,y=kx-----equation\text{ 1} \\ k=\frac{y}{x}----equation\text{ 2} \end{gathered}$

STEP 3: Find the value of the constant

By substitution,

$\begin{gathered} y=3,x=6 \\ Using\text{ equation 2} \\ k=\frac{y}{x}=\frac{3}{6}=\frac{1}{2} \\ \\ k=\frac{1}{2} \end{gathered}$

STEP 4: Find the value of y when x = 15

Using the equation 1

$\begin{gathered} y=kx \\ x=15 \\ \therefore y=\frac{1}{2}\times15=\frac{15}{2}=7\frac{1}{2}\text{ }or\text{ }7.5 \end{gathered}$

Hence, the value of y is

$\frac{15}{2}\text{ }or\text{ }7\frac{1}{2}\text{ }or\text{ }7.5$