Question

What number must be added to each term to the ratio 9 : 16 to make the ratio 2 : 3?

Answer 1

Let x be the required number.
Then, (9 + x) : (16 + x) = 2 : 3

$$\begin{gathered} \Rightarrow \frac{9+x}{16+x}=\frac{2}{3} \\ \Rightarrow 27+3x=32+2x\Rightarrow x=5 \end{gathered}$$

Hence, 5 must be added to each term of the ratio 9 : 16 to make it 2 : 3.