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Algebra Difficulty 1.5 Junior Find the answer Canada

A bag contains only green, yellow and red marbles. The ratio of green marbles to yellow marbles to red marbles in the bag is $3 : 4 : 2$ . If 63 of the marbles in the bag are not red, the number of red marbles in the bag is

$14$
$18$
$27$
$36$
$81$

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 the sum of the number of green marbles and the number of yellow marbles in the bag is 63.

Thus, $3n+4n=63$ 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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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.