Question

What number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?

What number must be added to each of the numbers 6, 15, 20 and 43 to give four numbers in proportion?

Answer 1

Let the number be x.

6 + x, 15 + x, 20 + x, 43 + x

⇒ 6 + x : 15 + x = 20 + x : 43 + x

⇒ `(6 + x)/(15 + x) = (20 + x)/(43 + x)`

⇒ (6 + x) (43 + x) = (15 + x) (20 + x)

Left side:

6 × 43 + 6x + 43x + x² = 258 + 49x + x²

Right side:

15 × 20 + 15x + 20x + x² = 300 + 35x + x²

⇒ 258 + 49x + x² = 300 + 35x + x²

⇒ 258 + 49x = 300 + 35x

⇒ 49x − 35x = 300 − 258

⇒ 14x = 42

⇒ x = 3

∴ The number to be added is 3.