Question

What number must be added to each of the numbers 4, 6, 8, 11 in order to get the four numbers in proportion?

Answer 1

Let x be added to make them in proportion.

∴ (4 + x) : (6 + x) :: (8 + x) : (11 + x)

⇒ `(4 + x)/(6 + x) = (8 + x)/(11 + x)`

⇒ (4 + x) (11 + x) = (6 + x) (8 + x)

Left side:

4 × 11 + 4x + 11x + x² = 44 + 15x + x²

Right side:

6 × 8 + 6x + 8x + x² = 48 + 14x + x²

⇒ 44 + 15x + x² = 48 + 14x + x²

⇒ 44 + 15x = 48 + 14x

⇒ 15x − 14x = 48 − 44

⇒ x = 4

∴ The number to be added is 4.