# Mathematics

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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 - ,

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 A-3, B has y+3
y+3 = 2(x-3)
y+3 = 2x - 6
2x - y = 9 , #1

B gives \$5 to A
A now has x-3 + 5 = x+2
B now has y+3 - 5 = y - 2

x+2 = 2(y-2)
x+2 = 2y - 4
x - 2y = -6 , #2

#1 times 2
---> 4x-2y=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(x-3)
y = 2x - 9

B gives \$5 to A
A has x+5, B has y-5
x+5 = 2(y-5)
x = 2y - 10 - 5
x = 2(2x-9) - 15
x = 4x - 33
-3x = -33
x = 11
y = 13

This too can be verified.