A box has 8 blue, \(x\) green, \((x-2)\) red and 10 black balloons. The probability of choosing a green balloon at random from the box is \(\frac{1}{4}\). What is the total number of green, red and black balloons?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 24
P(green) \(=\) green balloons ÷ all balloons. Writing both in terms of \(x\) gives one equation for \(x\).
All balloons \(=8+x+(x-2)+10=2x+16\)
\(\displaystyle \frac{x}{2x+16}=\frac{1}{4}\)
\(4x=2x+16\), so \(x=8\)
Green \(=8\), red \(=8-2=6\), black \(=10\)
Green \(+\) red \(+\) black \(=8+6+10=24\)