Discussion
In three coloured boxes - Red, Blue and Green, 90 balls are placed. There are twice as many balls in the Red and Blue boxes combined as there are in the Green box and there are twice as many balls in the Green box as there are in the Red box. How many balls are there in the Blue box ?
Answer: B
The Blue box has 45 balls.
Let the boxes hold \(R\), \(B\) and \(G\) balls. Red and Blue together are twice Green, and Green is twice Red:
\[ \begin{aligned} R + B &= 2G \\ R + B + G &= 90 \\ 3G &= 90,\ G = 30 \end{aligned} \]
\[ \begin{aligned} R &= G/2 = 15 \\ B &= 90 - 30 - 15 = 45 \end{aligned} \]
Check: Red and Blue together hold 60, twice Green's 30, and Green's 30 is twice Red's 15. The option 15 is the Red box and 30 the Green box, so they answer the wrong part of the question.
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