There are 200 red marbles and 90 white marbles in Box A. There were 80 red marbles and 100 white marbles in Box B. After some marbles were transferred from Box A to Box B, the ratio of red marbles to white marbles in Box A became 1:1 and the ratio of red marbles to white marbles in Box B became 3:2. What were the total number of marbles that were transferred from Box A to Box B?
+9519 Suppose that x red marbles and y white marbles were transferred to Box B.
\(\begin{cases}\dfrac{200-x}{90-y} = \dfrac11\\\dfrac{80+x}{100+y} = \dfrac32\end{cases}\)
You can simplify this:
\(\begin{cases}x - y = 110\\2x - 3y = 140\end{cases}\)
Then solve it with any method you like:
\(x = 190, y = 80\)
Therefore, a total of 270 marbles were transferred.
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