Question

What number must be added to each of the numbers 6, 14 and 30 so that the resulting numbers may be in continued proportion?

Answer 1

Let the number to be added to each be x.

6 + x, 14 + x, 30 + x

Three numbers to be in continued proportion:

⇒ `(6 + x)/(14 + x) = (14 + x)/(30 + x)`

⇒ (6 + x) (30 + x) = (14 + x) (14 + x)

Left side:

(6 + x) (30 + x) = 180 + 6x + 30x + x² = 180 + 36x + x²

Right side:

(14 + x)² = 196 + 28x + x²

We get:

⇒ 180 + 36x + x² = 196 + 28x + x²

⇒ 180 + 36x = 196 + 28x

⇒ 36x − 28x = 196 − 180

⇒ 8x = 16

⇒ x = 2

∴ The number to be added is 2.