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?
+184 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!
+6 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.
