Problem
ALG-B1-M06-P010 Recovering a ratio
#10
★★☆☆☆ Level 2 of 5
Let \(a,b>0\) and \(\frac{a-b}{a+b}=\frac{1}{3}\). Find \(\frac{a}{b}\).
Set \(t=\frac{a}{b}\).
After dividing numerator and denominator by \(b\), we get \(\frac{t-1}{t+1}=\frac{1}{3}\). Thus \(3t-3=t+1\), so \(2t=4\) and \(t=2\).
A short problem on replacing scale by a ratio.