Charlie and David collect marbles.the ratio of Charlie's marbles to David's marbles is 2:7.David gave Charlie some of his marbles and now David has twice as many marbles as Charlies.if Charles now has 24 marbles how many marbles did David give him?

Let the number of marbles Charlie has initially be C and David, D. C/D=2/7, so D=7C/2. Let x be the number of marbles David gives Charles, so David has D-x=7C/2-x and Charles has C+x. So 7C/2-x=2(C+x). C+x=24, so 7C/2-x=48, therefore 7C-2x=96. But C=24-x, so 168-7x-2x=96, and 9x=168-96=72, making x=8. Therefore, David gave 8 marbles to Charles.

Check: C=24-8=16 and D=7*16/2=56. David gives 8 marbles to Charles leaving 48 and Charles has 24, half as many as David. OK!

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