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A box contains some red, blue and white marbles. There is a total of 65 red marbles and blue marbles. There is a total of 35 red marbles and white marbles. The number of blue marbles is thrice the number of white marbles. What fraction of the marbles is red?

May 11, 2021

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A box contains some red, blue and white marbles. There is a total of 65 red marbles and blue marbles. There is a total of 35 red marbles and white marbles. The number of blue marbles is thrice the number of white marbles. What fraction of the marbles is red?

I think there’s a typo - It should say what fraction of the marbles are red, but never mind that… haha

Let $r, b, w \in \text{red, blue, white}.$

$r+b = 65. (1)$

$r+w = 35. (2)$

$b=3w. (3)$

(2) & (3) $\Rightarrow r+3w = 65. (4)$

$\frac{(4) - (2)}{2} \Rightarrow \frac{2w}{2} = 30 \div 2 \Rightarrow w = 15 (5)$

(5) & (3) $\Rightarrow b = 45 (6)$

(6) & (1)$\Rightarrow r = 20 (7)$

Steps to get desired answer: $\frac{(7)}{(7)+(6)+(5)} \Rightarrow \frac{20}{20+45+15} \Rightarrow \frac{20}{80} = \frac{1}{4}.$

Thus, the answer is $\boxed{\frac{1}{4}}$

May 11, 2021