Money Trading

[MAS1]

Daniel says to Sydney, "If you give me $2 of your money, we will each have the same amount of money." Sydney responds, "That's true, but on the other hand if you give me $2 of your money, I will have twice as much money as you."

Question: How much money did Daniel and Sydney each have?

[noreply]

Daniel says to Sydney, "If you give me $2 of your money, we will each have the same amount of money." Sydney responds, "That's true, but on the other hand if you give me $2 of your money, I will have twice as much money as you."

Question: How much money did Daniel and Sydney each have?

Let Daniel's money be d, Sydney's money be s.

d + 2 = s - 2
2(d - 2) = s + 2

Simultaneously solve the equations:
d = s - 4
2((s - 4) - 2) = s + 2
2(s - 6) = s + 2
2s - 12 = s + 2
s - 12 = 2
s = 14

Sub it in:
d + 2 = 14 - 2
d + 2 = 12
d = 10.

Sydney has $14, Daniel has $10.

[MAS1]

You are right!