ratio and proportion

Algebra Level 2

$a,b$ and $c$ are positive numbers. The ratio of $c$ to $a$ is equal to the ratio of $a$ to $b$ . If $c=2$ when $a=1$ , what is $a^2$ when $c=8$ ?

1 solution

A Former Brilliant Member
Sep 24, 2017

$\dfrac{c}{a}=\dfrac{a}{b}$ $\implies$ $\dfrac{2}{1}=\dfrac{1}{b}$ $\implies$ $b=\dfrac{1}{2}$

When $c=8$ , we have

$\dfrac{8}{a}=\dfrac{a}{\dfrac{1}{2}}$ $\implies$ $a^2=8\left(\dfrac{1}{2}\right)$ $\implies$ $\color{#D61F06}\boxed{a^2=4}$