+1859 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?
+129771 A = what Alice has at first
B = what Bob has at first
(A + n) = 10(B - n) → A + n = 10B - 10n → A -10B = -11n (1)
(A - n) = 4 (B + n) → A - n = 4B + 4n → A - 4B = 5n (2)
Multiply (1) by 5 and (2) by 11
5A - 50B = -55n
11A - 44B = 55n add these
16A - 94B = 0
16A = 94B
A / B = 94 / 16 = 47 / 8
