Question

Find whether the numbers $6,10,14and22$ are in proportion or not. If not, what must be added to each of the numbers so that they become proportional?

Answer 1

Step 1-Find the proportionality:

$$\begin{gathered} 6,10,14,22 \\ so,\frac{6}{10}=\frac{3}{5} \\ \frac{14}{22}=\frac{7}{11} \\ \frac{6}{10}\ne \frac{14}{22} \end{gathered}$$

so they are not in proportion

Step 2-Find the term to be added:

if the numbers are in proportion

$\frac{6+x}{10+x}=\frac{14+x}{22+x}$

cross multiply

$$\begin{gathered} (6+x)·(22+x)=(14+x)·(10+x) \\ 132+x^2+22x+6x=140+14x+10x+x^2 \\ 132+28x=140+24x \\ 4x=8 \\ x=2 \end{gathered}$$

Hence the numbers are not in proportion and the number to be added for the numbers $6,10,14and22$ to be proportional is $2$.