Question 54

What number must be added to each of the number 7,4 and 2 so that the resulting number may be in a continued proportion?

Solution

Let's assume the number can be added to make a continued proportion is 'y'.

$$\frac{7+y}{4+y}\ =\ \frac{4+y}{2+y}$$

(7+y) (2+y) = (4+y) (4+y)

$$14+7y+2y+y^2=y^2+8y+16$$

14+9y = 8y+16

9y-8y = 16-14

y = 2

So 2 can be added to make a continued proportion.

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