# If a/b=4/3 and b/c=2/3, what is the value of 2b/a+b-c?

## I am having a hard time solving this. Also, can you give me a simple, fast way to answer this question?

Jun 20, 2017

See below.

#### Explanation:

Since $\frac{a}{b} = \frac{4}{3}$, then $\frac{b}{a} = \frac{3}{4}$.

Since $\frac{b}{c} = \frac{2}{3}$, $3 b = 2 c$, and $b = \frac{2}{3} c$ (or $c = \frac{3}{2} b$).

Now we plug things in.

$2 \frac{b}{a} + b - c = 2 \left(\frac{3}{4}\right) + \frac{2}{3} c - c = \frac{3}{2} - \frac{1}{3} c$ or $2 \frac{b}{a} + b - c = 2 \left(\frac{3}{4}\right) + b - \frac{3}{2} b = \frac{3}{2} - \frac{1}{2} b$