Question

If the same number be added to the numbers 5, 11, 15 and 31, the resulting numbers are in proportion. Find the number.

Answer 1

Let x be added to each number, then the numbers will be 5 + x, 11 + x, 15 + x and 31 + x

According to the condition,

$\frac{5+x}{11+x}=\frac{15+x}{31+x}$

By cross multiplication,

(5+x)(31+x)=(15+x)(11+x)

$\Rightarrow$155+5x+31x+$x^2$=165+11x+15x+$x^2$

$\Rightarrow 155+36x+x^2=165+26x+x^2$

$\Rightarrow 36x+x^2-26x-x^2=165-155$

$\Rightarrow 10x=10\Rightarrow x=\frac{10}{10}=1$

$\therefore$ 1 should be added