Question

What number should be added to each of the numbers 3,5,13,19 so that the resulting number may be in proportion.

Answer 1

Annyeonghaseyo

Let the number be x.

So,

(19+x)+x(19+x)=13(5+x)+x(5+x)

57+3x + 19x + ${x}^{2}$= 65+13x +5x + ${x}^{2}$

57 + 22x + ${x}^{2}$ = 65+ 18x + ${x}^{2}$

22x - 18x + ${x}^{2}$ - ${x}^{2}$= 65- 57

8/4 = x

2 =$\texttt{x}$

so the required has to be added to make it proportion is $\texttt{2}$