CEMC Cayley

Algebra Difficulty 2.3 Junior Find the answer

If a bag contains only green, yellow, and red marbles in the ratio $3: 4: 2$ and 63 of the marbles are not red, how many red marbles are in the bag?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since the ratio of green marbles to yellow marbles to red marbles is $3: 4: 2$ , then we can let the numbers of green, yellow and red marbles be $3n, 4n$ and $2n$ for some positive integer $n$ . Since 63 of the marbles in the bag are not red, then $3n+4n=63$ and so $7n=63$ or $n=9$ , which means that the number of red marbles in the bag is $2n=2 \times 9=18$ .

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