Question

If y=12 when x=15, what is x when y=21?

Answer 1

If y varies directly with x then

`\begin{gathered} y=kx \\ \text{ Where k is a constant of a variation} \end{gathered}`

First, we need to find the constant of a variation k, for this, we use the given values of x and y:

`\begin{gathered} y=kx \\ 12=k\cdot15 \\ \text{ Divide by 15 from both sides of the equation} \\ (12)/(15)=(k\cdot15)/(15) \\ (12)/(15)=k \\ \text{ Simplifying} \\ (3\cdot4)/(3\cdot5)=k \\ (4)/(5)=k \end{gathered}`

Then since we already have the value of k we can find the value x when y = 21:

`\begin{gathered} y=kx \\ 21=(4)/(5)x \\ \text{ Multiply by 5 from both sides of the equation} \\ 5\cdot21=5\cdot(4)/(5)x \\ 105=4x \\ \text{ Divide by 4 from both sides of the equation} \\ (105)/(4)=(4x)/(4) \\ (105)/(4)=x \end{gathered}`

Therefore, if y = 12 when x = 15, then

`x=(105)/(4)`

when y = 21.