Mathematical Riddle!?

Question

I need help to solve this riddle.

Person A has one amount of money in his pocket, Person B has one amount in his pocket.

If person A gives person B X amount from his pocket, person B will end up with 3 times more money in his pocket than person A.

However if person B gives person A the X amount of money person A will end up with 2 times more money than person B in his pocket.

How much does each guy have in his pocket, and how much is X???

Can someone help me solve this riddle??

Answer 1

Here's a start...

A - X = 1/3 (B+X)

and

B-X = 1/2 (A + X)

Go from there... can you get it now?

Answer 2

A has $1. B has $2

Answer 3

This problem is impossible. You need one more piece of information to get a definitive answer, such as how much money there is total - or one more hypothetical fact.

You can, however, solve the riddle in terms of the other values. The solution is: x=(5/11)A, x=(5/13)B, A=(11/13)B

In other words, x (the amount transferred) is 5/11 of Person A's original amount and 5/13 of Person B's original amount. Person A begins with 11/13 of the amount Person B does.

You can get to this by starting with these equations:
(A-x)*3 = B+x
(A+x) = (B-x)*2
where A is Person A's original amount and B is Person B's original amount. Therefore (A-x) represents how much Person A has after giving away $x and (B+x) is how much Person B has after receiving $x. You can solve these equations for the variables in terms of each other but cannot reach a definite answer without another piece of information.

Answer 4

M = amount person A has
N = amount B has
X = amount of money given from one to the other

3*(M - X) = N + X
M + X = 2*(N - X)

There are 3 variables and only 2 equations so a definite solution is not possible. However you can solve for two of the variables in terms of the third as is done below.

3M - 3X = N + X or N = 3M - 4X
M + X = 2N - 2X or N = (M + 3X)/2

3M - 4X = (M + 3X)/2

M = 11X/5 N = 13X/5

3*(M - X) = N + X .... 18/5 = 18/5
M + X = 2*(N - X) .... 16/5 = 16/5

X can be anything and M = 11X/5 and N = 13X/5

There must be some other condition if you want definite values for each of these.

Answer 5

Okay buddy,

This is how I belive you solve the problem:

The word problem can be modeled by the equations:

B + X = 3A (1)

A + X = 2B (2)

from (2) we can see that X = 2B - A

then combining equations (1) and (2)

B + 2B - A = 3A

yields,

3B = 4A

thus,

B =(4A)/3

So B is 133.33% of A

For exampe if person A has 3 dollars, person B will have 4 dollars according to the above equations.

Then,

from (1) 4 + X = 9

yields X=5

and,

from (2) 3 + X = 8

yields X=5

So X is a variable dependant on B and A, and varies as A and B change. It may be helpful to not that X is always 5/4 of B and 5/3 of A.

Hope this helps

Answer 6

This is unsolvable, you have 3 variables and 2 equations. You will end up with a range of solutions.

Added:

There will be multiple solutions, but here is one:
A = 11
B = 13
X = 5

Answer 7

Let's let a and b be the starting amounts of persons a and b.

b+x=3(a-x)
a+x=2(b-x)

Now we only have two equations and they have 3 variables so we can't solve them.

Answer 8

A = A's money
B = B's money

3(A - X) = B
2(B - X) = A

3A - 3X = B
2B - 2X = A

-6A + 6X = -2B
6B - 6X = 3A
-6A + 6B = 3A - 2B
8B = 9A
B = (9/8)A

This has more than one solution, but here is one:
A = 8
B = 9

2(9 - X) = 8
3(8 - X) = 9

18 - 2X = 8
24 - 3X = 9

-2X = -10
X = 5

-3X = -15
X = 5

So A has 8, B has 9, and X=5

Answer 9

This subject has been asked maximum of circumstances right here, you have looked for it. there's no lacking funds. you may no longer upload bills to funds lower back to them, considering that your debt is going down, no longer up: £40 9 + £40 9 - £a million = £ninety seven = cost of purchase nevertheless: unique quantity borrowed: £50 + £50 = £a hundred Disbursement of this funds: £ninety seven (for notwithstanding replaced into offered) £a million (to mum) £a million (to dad) £a million (earnings pocket finally lower back to human beings) ------- £a hundred

Answer 10

3(A - X) = B + X
A + X = 2(B - X)

3A - 3X = B + X
A + X = 2B - 2X

3A - B = 4X
A - 2B = -3X

9A - 3B = 12X
4A - 8B = -12X

13A - 11B = 0

There are infinitely many answers... Here's one:
A = 11
B = 13
X = (3A - B)/4 = 20/4 = 5

If you want only integer solutions, all solutions are of the form:
A = 11n
B = 13n
X = 5n
where n is an integer.