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# solve

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Alice and Bob each have a certain amount of money. If Alice receives n dollars from Bob, then she will have 4 times as much money as Bob. If, on the other hand, she gives n dollars to Bob, then she will have 8 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?

Jun 21, 2023

### 2+0 Answers

#1
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https://web2.0calc.com/questions/gt-algebra-1-lt-alice-and-bob-each-have-a-certain

this should give you an idea of how to do it, with a very similar problem. Just use different numbers!

Jun 22, 2023
edited by HumenBeing  Jun 22, 2023
#2
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Let's assume Alice has A dollars and Bob has B dollars.

According to the first condition, if Alice receives n dollars from Bob, Alice will have A + n dollars, and she will have 4 times as much money as Bob: A + n = 4B.

According to the second condition, if Alice gives n dollars to Bob, Alice will have A - n dollars, and she will have 8 times as much money as Bob: A - n = 8B.

To find the ratio of the amount of money Alice has to the amount Bob has, we need to find A/B.

Now, we can solve the system of equations:

A + n = 4B A - n = 8B

Adding the two equations, we get:

2A = 12B A = 6B

Now we know that the ratio of the amount of money Alice has to the amount Bob has is 6:1, or simply 6. Therefore, Alice has 6 times the amount of money Bob has.

Jun 22, 2023