You can make two equations here. First, you know the total number of marbles is 103, so:
The second equation is more complicated, so let’s do it in parts. First, he gives away 15 red marbles, so he should have r – 15 left. He gives away 2/5 of his blue marbles, so he should have b – 2/5b = 3/5b left.
So the ratio of red marbles he has left to blue marbles he has left (which the question tells us is 3/7) should be:
The question asks how many blue marbles he had originally, so let’s substitute and solve for b. First get r by itself in the first equation:
Now substitute that into the second equation and solve:
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