Question

The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\dfrac{12}{23}$, find the total number of balls in the given bag.

Hint:

Translate word problems into equations by defining variables clearly and use cross-multiplication in probability.

Answer 1

Let the number of black balls be $x$.
Then, the number of red balls = $x + 3$
Total number of balls = $x + (x + 3) = 2x + 3$
Given: \[ \frac{\text{Number of red balls}}{\text{Total number of balls}} = \frac{12}{23} \Rightarrow \frac{x + 3}{2x + 3} = \frac{12}{23} \] Cross-multiplying: \[ 23(x + 3) = 12(2x + 3)\\ 23x + 69 = 24x + 36\\ 69 - 36 = 24x - 23x \Rightarrow x = 33 \] Total number of balls = $2x + 3 = 2(33) + 3 = 69$
Answer: Total number of balls in the bag = 69