Question

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

Answer 1

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=(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=(y)/(x)=(3)/(6)=(1)/(2) \\ \\ k=(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=(1)/(2)*15=(15)/(2)=7(1)/(2)\text{ }or\text{ }7.5 \end{gathered}`

Hence, the value of y is

`(15)/(2)\text{ }or\text{ }7(1)/(2)\text{ }or\text{ }7.5`