Posted by Diamon on .
If A gives B $3, B will have twice as much as A. If B gives A $5, A will have twice as much as B. How much does each have? Explain clearly your working.

Mathematics 
Reiny,
A now has x
B now has y
The wording is confusing.
Are the consecutive transfers of money, or are they independent events
Case1 : consecutive events
A gives $3 to b
A now has A3, B has y+3
y+3 = 2(x3)
y+3 = 2x  6
2x  y = 9 , #1
B gives $5 to A
A now has x3 + 5 = x+2
B now has y+3  5 = y  2
x+2 = 2(y2)
x+2 = 2y  4
x  2y = 6 , #2
#1 times 2
> 4x2y=18
#2 > x  2y = 6
subract:
3x = 24
x = 8
then y = 7
A has $8 and B has $7
first transfer, A give $3 to B
A has 5 , and B has 10 , Does B have twice A ? yup
2nd transfer , B gives $5 to A
A has 10 , B has 5, does A have twice of B ? , yup
Case 2: independent events:
A gives $3 to B
y+3 = 2(x3)
y = 2x  9
B gives $5 to A
A has x+5, B has y5
x+5 = 2(y5)
x = 2y  10  5
x = 2(2x9)  15
x = 4x  33
3x = 33
x = 11
y = 13
This too can be verified.
Pick your interpretation.