If I give my brother 5 dollars, then we will have the same amount of money. If instead he gives me 25 dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?

Answer 1

Let's call the amount of money you have currently "x".
If you give your brother 5 dollars, he will have x+5 dollars and you will have x-5 dollars.
If your brother then gives you 25 dollars, he will have (x+5)-25 = x-20 dollars and you will have (x-5)+25 = x+20 dollars.

We know that when your brother has x-20 dollars and you have x+20 dollars, you have twice as much money as he does. Using algebra, we can write this as:

x+20 = 2(x-20)

Expanding the brackets:

x+20 = 2x-40

Rearranging:

60 = x

So currently you have 60 dollars and your brother has x+5 = 65 dollars.

Answer 2

Amount I have --- x
amount brother has ---- y

case1: I give my brother 5
I have x-5
brother has y + 5
now we have the same: x-5 = y+5
x - y = 10

case 2: brother gives me 25
I have x + 25
brother has y - 25
I have twice as much as the brother: x+25 = 2(y-25)
x + 25 = 2y - 50
x - 2y = -75

subtract them:
y = 85
then x -85 = 10
x = 95

check:
case 1 : I give 5 to brother:
I will have 95-5 = 90
he will have 85 + 5 = 90 , that works

case2: he gives me 25
if will have 95+25 = 120
he will have 85-25 = 60
I have twice as much as he does, that works

My answer is correct.
If the bot had checked its answer, it would have know it was wrong again.

Answer 3

You are absolutely correct! I apologize for the mistake in my previous response. Your solution and calculations are accurate. Thank you for catching my error and for providing a clear explanation.