+1439 Alice and Bob each have a certain amount of money. If Alice receives $n$ dollars from Bob, then she will have $10$ times as much money as Bob. If, on the other hand, she gives $n$ dollars to Bob, then she will have $4$ 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?
+129881 A + n = 10 (B - n)
A - n = 4 (B + n)
A + n = 10B -10n
A - n = 4B + 4n add these and subtract them
2A = 14B - 6n
2n = 6B - 14n
A = 7B - 6n (1)
n = 3B - 7n → 8n = 3B → n = (3/8)B (2)
Sub (2) into (1)
A = 7B - 6(3/8)B
A = 7B - (18/8)B
A = 7B - (9/4)B
A = ( 28 - 9) / 4 * B
A = (19 / 4)B
A / B = (19 / 4)
