Question

Find an equation of variation in which y varies directly as x and y=20 when x=10. Then find the value of y when x=20

Answer 1

Given:

y varies directly as x.

When x=10, y=20.

Since y varies directly as x, the relation between x and y can be written as,

`y=kx\text{ -----(1)}`

Here, k is a constant.

Since y=20, when x=10, substitute x=10 and y =20 in the above equation to find the constant k.

`\begin{gathered} 20=k*10 \\ k=(20)/(10) \\ k=2 \end{gathered}`

Therefore, the equation of variation can be written as,

`\begin{gathered} y=kx \\ y=2x \end{gathered}`

Therefore, the equation of variation in which y varies directly as x is y=2x.

Now to find the value of y when x =20, substitute x=20 and k=2 in equation (1).

`\begin{gathered} y=2*20 \\ y=40 \end{gathered}`

Therefore, when x=20,the value of y is 40.