Question

what number must be added to each of the number 5,6,7,12, to get the number which are in proportion

Answer 1

consider x as no to be added

so (6+x)/(14+x)=(18+x)/(38+x)

(6+x)(38+x)=(18+x)(14+x)

228 +44x +x^2 = 252+32x +x^2

12x = 24

x=2

answer = 2

Answer 2

$\textbf{Let x should be added, } \\ \\ \\ \textbf{ According to the question, if x is added to each number they will be in proportion. } \\ \\ \\ = > \frac{5 + x}{6 +x } = \frac{7 + x}{12 + x} \\ \\ \\ = > (5 + x)(12 + x) = ( 7 + x)(6 + x) \\ \\ = > 60 + 5x+ 12x + {x}^{2} = 42 + 7x + 6x + {x}^{2} \\ \\ \\ = > 60 + 17x = 42 + 13x \\ \\ \\ = > 4x = - 18 \\ \\ = > x = - \frac{9}{2}$

- 9 / 2 should be added.