Question

If $x+7;2(x+14)$ in the duplicate ratio of $5:8$, find $x$.

Answer 1

Duplicate ratio of two numbers, means the ratio of their squares

So the duplicate ratio of $5:8$ is $25:64$

Given that the duplicate ratio of $5:8$ is $x+7:2(x+14)$

$\Rightarrow \frac{x+7}{2(x+14)}=\frac{25}{64}$

$\Rightarrow 32(x+7)=25(x+14)$

$\Rightarrow 32x-25x=350-224$

$\Rightarrow 7x=126$

$\Rightarrow x=18$

Therefore the value of $x$ is $18$