Question

There are $30$ blue balls and $x$ red balls in a bag. A ball is drawn at random from the bag.
Given that the probability is $\frac{7}{13}$, find $x$.

Answer 1

Blue balls $=30$

Red balls $=x$

Total balls $=30+x$

Probability of red balls $=\frac{x}{30+x}$

According to question, $\frac{x}{30+x}=\frac{7}{13}\Rightarrow 13x=210+7x$

$=6x=210$

$x=35$