Alice and Bob each have a certain amount of money. If Alice receives n dollars from Bob, then she will have 4 times as much money as Bob. If, on the other hand, she gives n dollars to Bob, then she will have 8 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?
+2 This is quite interesting so here is my answer: octordle unlimited
Let's denote:
A = the amount of money Alice currently has. B = the amount of money Bob currently has.
Given in the problem:
If Alice receives n dollars from Bob, she will have 4 times as much money as Bob. This means A + n = 4(B - n). If Alice gives n dollars to Bob, she will have 8 times as much money as Bob. This means A - n = 8(B + n).
Now we have two equations, and we can solve for n in terms of A and B:
n = (A - 4B) / 5
n = (A - 8B) / -7
Since both expressions equal n, we can equate and solve for the ratio of A to B:
(A - 4B) / 5 = (A - 8B) / -7
Solving this equation gives us:
-7A + 28B = 5A - 40B 12A = 68B A/B = 68/12 = 17/3
So, the ratio of the amount of money Alice has to the amount Bob has is 17:3.
