Question

Suppose yvaries directly as x and $y=14$when $x=4$. What is the value of y when $x=9$?

A 25.5

B 27.5

C 29.5

D 31.5

Short answer

The value of y is 31.5 .Option D is correct.

Step-by-step solution

Step 1. State the concept of Direct Proportionality.

Direct proportion is a mathematical comparison between two numbers where the ratio of the two numbers is equal to a constant value. The proportion definition says that when two ratios are equivalent, they are in proportion. The symbol used to relate the proportions is "$\propto$".

Here yvaries directly as x.

That is, $y\propto x$

Therefore$y=kx$ … (1)

where kis a constant.

Step 2. Find the value of Constant ‘k’.

Find the value of k by substituting $y=14\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}x=4$in equation $y=kx$.

$\begin{array}{c}14=k.\left(4\right)\\ \frac{14}{4}=\frac{4k}{4}\\ \frac{7}{2}=k\\ k=\frac{7}{2}\end{array}$

Step 3. Calculate the value of ‘y’.

Calculate the value of y by substituting $x=9\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}y=\frac{7}{2}$in $y=kx$.

$\begin{array}{c}y=\frac{7}{2}\times 9\\ y=\frac{63}{2}\\ y=31.5\end{array}$

Thus the value of yis 31.5.

Hence option D is correct.