# Suppose that y varies directly as the square root of x and that y = 49 when x = 81. What is y...

## Question:

Suppose that y varies directly as the square root of x and that y = 49 when x = 81. What is y when x = 207?

## Direct Proportion

Two quantities can be said to be in direct proportion with each other when both increase and decrease at the same time. For example, the amount of fuel required is directly proportional to the distance to be driven.

As y varies directly as the square root of x, we have:

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

When x=81, y=49. So,

\begin{align} 49&=k\sqrt{81}\\ 49&=9k\\ k&=\frac{49}9 \end{align}

So,

$$y=\frac{49}9\sqrt{x}$$

When x=207, the value of y will be:

\begin{align} y&=\frac{49}9\sqrt{207}\\ &=78.33 \end{align}