Question

2) Find the ratio of a to b
10/21 = 2a/a+b
A) 41/10
B) 10/13
C) 1/13
D) 5/16

Answer 1

\[\frac{2a}{a+b} = \frac{10}{21}\]

Answer 2

First take reciprocals both the sides..

\[\frac{a+b}{2a} = \frac{21}{10}\]

Answer 3

Now separate the terms on left side, with having equal denominators like this:

\[\frac{a}{2a} + \frac{b}{2a} = \frac{21}{10}\]

You can cancel \(a\) with \(a\).. :)

Answer 4

\[\frac{1}{2} + \frac{b}{2a} = \frac{21}{10} \implies \frac{b}{2a} = \frac{21}{10} - \frac{1}{2} \implies \frac{b}{2a} = \frac{21-5}{10}\]

Answer 5

\[\frac{b}{2a} = \frac{16}{10} \implies 2 \times \frac{b}{2a} = 2 \times \frac{16}{10} \implies \frac{b}{a} = \frac{16}{5}\]

Answer 6

Just take the reciprocals again to get the ratio \(a:b\)