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?

parmen Jan 1, 2024

#1**+1 **

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

CPhill Jan 2, 2024