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# HeLp PlS

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Alice and Bob each have a certain amount of money. If Alice receives  dollars from Bob, then she will have  times as much money as Bob. If, on the other hand, she gives  dollars to Bob, then she will have  times as much money as Bob. If neither gives the other any money, what is the ratio of the amount of money Alice has to the amount Bob has?

The answer is not 17/7 i tried

Anyways thanks for your help!

Nov 2, 2023

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Let Alice's initial amount of money be a and Bob's initial amount of money be b.

If Alice receives x dollars from Bob, then she will have a+x dollars and Bob will have b−x dollars. Therefore, a+x is 2×(b−x), so 3x=2b−a.

If Alice gives y dollars to Bob, then she will have a−y dollars and Bob will have b+y dollars. Therefore, a−y is 3×(b+y), so 4y=3a−3b.

Subtracting the first equation from the second equation, we get y=a−2b. Substituting this into the first equation, we get 3(a−2b)=2b−a, so 5a=7b.

Therefore, the ratio of Alice's amount of money to Bob's amount of money is 7:5​.

Nov 2, 2023