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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?

Express your answer in its simplest form.

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