Question

What number must be added to each of the numbers 5, 9, 7, 12 to get the numbers which are in proportion?

Answer 1

Suppose that the number is x.

Then, (5 + x) : ( 9 + x) :: (7 + x) : (12 + x)

$$\begin{gathered} \Rightarrow (5+x)\times (12+x)=(9+x)\times (7+x)(\mathrm{Product}\mathrm{of}\mathrm{extremes}=\mathrm{Product}\mathrm{of}\mathrm{means}) \\ \Rightarrow 60+5x+12x+x^2=63+9x+7x+x^2 \\ \Rightarrow 60+17x=63+16x \\ \Rightarrow x=3 \end{gathered}$$

Hence, 3 must be added to each of the numbers: 5, 9, 7 and 12, to get the numbers which are in proportion.