Question

what must be added to numbers1,3,10,18 so that they are inproportion?

Answer 1

let the x be added

(1+x)/(3+x) = (10+x)/(18+x)

⇒(1+x)(18+x) = (3+x)(10+x)

⇒18+x+18x+x² = 30+10x+3x+x²

⇒18+19x+x² =30+13x+x²

⇒6x = 30- 18 = 12

⇒x = 2

Answer 2

let the x be added

(1+x)/(3+x) = (10+x)/(18+x)

⇒(1+x)(18+x) = (3+x)(10+x)

⇒18+x+18x+x² = 30+10x+3x+x²

⇒18+19x+x² =30+13x+x²

⇒6x = 30- 18 = 12

⇒x = 2