Question

What number must be added to each of the numbers $5,11,19,37$ so they are in proportion ?

Answer 1

Finding the number that should be added:

$5,11,19,37$

according to the equation

$\frac{5+x}{11+x}=\frac{19+x}{37+x}$

cross multiply

$$\begin{gathered} (5+x)·(37+x)=(19+x)·(11+x) \\ 185+37x+5x+x^2=209+19x+11x+x^2 \\ 185+42x=209+30x \\ 12x=24 \\ x=2 \end{gathered}$$

Hence the number that should be added so that the numbers $5,11,19,37$ are in proportion is $2$.