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?
+120 Let us say that Alice = a, and Bob = b
a + n = 4 ( b - n ) → this would be the equation for the first situation, now let us simplify.
a + n = 4b - 4n →. a = 4b - 5n → this would be the simplified version
Substitute ( a = 4b -5n ) into the equation
a - n = 8 ( b + n ) → 4b - 5n - n = 8b + 8n → 4b - 6n = 8b + 8n. → 4b + 2n = 8b → 2n = 4b n = 2b
Substitute ( n = 2b ) into the first equation
a = 4b - 5 ( 2b )
a = 4b - 10b
a = -6b
thus the ratio would be a: b = -6: 1
this answer does not seem correct, however if anyone wants to correct me they can 
+1237
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?
(A + n) = 4 • (B – n)
A + n = 4B – 4n
A – 4B = –5n (1)
(A – n) = 8 • (B + n)
A – n = 8B + 8n
A – 8B = 9n (2)
Multiply both sides
of (1) by 9 9A – 36B = –45n (3)
Multiply both sides
of (2) by 5 5A – 40B = 45n (4)
Add (3) and (4) 14A – 76B = 0
Add 76B to both sides 14A = 76B
Divide both sides by 76B
14A 1
–––– = ––
76B 1
Multiply both sides by 76/14
A 76 38
––– = ––– reduces to –––
B 14 7
It works if you accept the
concept of negative money.
That is, n must equal –2 dollars.
Say Alice has 38 and Bob has 7
(38 + n) = 4 • (7 – n)
38 + n = 28 – 4n
5n = –10
n = –2
and
(38 – n) = 8 • (7 + n)
38 – n = 56 + 8n
–9n = 18
n = –2
.
