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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