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?

tomtom Jan 11, 2024

#1**+1 **

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

CPhill Jan 11, 2024