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# Fraction and Ratios

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There are red marbles and yellow marbles in a bowl. The ratio of the number of red marbles to the blue marbles is 1:3. After 10 red marbles are added into the bowl and 10 blue marbles are removed from the bowl, the ratio of the number of red marbles to the blue marbles is 2:1. How many marbles were there in the bowl at first?

Jun 8, 2022

#1
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I am assuming there are only red and blue marbles in the bowl.

Let r and b be the amount of red and blue balls in the bowl respectively.

We have the system:

$${r \over b} = {1 \over 3}$$

$${{r + 10} \over {b - 10}} = 2$$

From the first equation, we have $$3r = b$$

Substituting this into the second equation and then solving, we find $$b = 18$$, meaning $$r = 6$$

Thus, the total amount of balls in the bowl is $$18 + 6 = \color{brown}\boxed{24}$$

Jun 8, 2022
#2
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Le the number of red marble in the bowl were x

and blue marble in the bowl were 3x

(x + 10)/(3x - 10) = 2/1

=> x + 10 = 6x - 20

-5x = -30

x = 6

Red marble were 6

Blue marble were 6 * 3 = 18

18 + 6 = 24 marble in the bowl

Jun 9, 2022