Alice and bob each have a certain amount of money. if alice receives $n$ dollars from bob, then she will have 3 times as much money as bob. if, on the other hand, she gives $n$ dollars to bob, then she will have 2 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?

Question

Business

Brylee Nichols

23 December, 21:41

Alice and bob each have a certain amount of money. if alice receives $n$ dollars from bob, then she will have 3 times as much money as bob. if, on the other hand, she gives $n$ dollars to bob, then she will have 2 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?

+3

Answers (1)

Know the Answer?

Alijah Alexander · Answer 1

Let x = Alice’s original amount of money,

y = Bob’s original amount of money

And n = the dollars they are referring to

So, the equation are:

If Alice receives dollars from Bob, then she will have 3 times as much money as Bob,

x + n = 3 (y - n)

x + n = 3y - 3n

x = 3y-3n-n

x = 3y - 4n

And if Alice give dollars to Bob, the she will have 2 times as much money as Bob,

x - n = 2 (y + n)

x - n = 2y + 2n

x = 2y + 2n + n

x = 2y + 3n

As, x = x

So, 3y - 4n = 2y + 3n

3y = 2y + 3n + 4n

3y - 2y = 3n + 4n

Y = 7n

Find x in terms of n also,

x = 2y + 3n, replace y with 7n

x = 2 (7n) + 3n = 14n + 3n

x = 17n

If neither gives the other any money, the ratio of the amount of money Alice has to the amount Bob has = x/y

Replace x and y with their values, x = 17n and y = 7n

= 17n / 7n

The ratio is 17:7