Question

What should be added to each of the numbers $13,17$ and $22$ so that, the resulting numbers are in continued proportion?
[3 Marks]

Answer 1

Let the required number to be added is $x$.

$\therefore$ $13+x,17+x$ and $22+x$ are in continued proportion. [ 1 Mark]

$\Rightarrow \frac{13+x}{17+x}=\frac{17+x}{22+x}$

$\Rightarrow (13+x)(22+x)=(17+x{)}^2$ [Cross multiplication] [ 1 Mark]

$\Rightarrow 286+35x+x^2=289+34x+x^2$

$\Rightarrow 35x-34x=289-286$

$\Rightarrow x=3$

$\therefore$ The number to be added is $3$. [1 Mark]