+1557 Alice and Bob each have a certain amount of money. If Alice receives $n$ dollars from Bob, then she will have $7$ times as much money as Bob. If, on the other hand, she gives $n$ dollars to Bob, then she will have $2$ 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?
+129895 If Alice receives $n$ dollars from Bob, then she will have $7$ times as much money as Bob.
A + n = 7 ( B - n) (1)
If, on the other hand, she gives $n$ dollars to Bob, then she will have $2$ times as much money as Bob
A - n = 2 ( B + n) (2)
Subtract (2) from (1)
2n = 5B - 9n
11n = 5B
n = (5/11)B
Using (1)
A + (5/11)B = 7 (B - (5/11)B)
A + (5/11)B = 7B - (35/11)B
A = 7B - (40/11)B
A = (37/11)B
A / B = 37 / 11
