If I give my brother 5 dollars, then we will have the same amount of money. If instead he gives me 24 dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?
x=What you started with
y=What your brother started with
[x - 5]=[y + 5]....................................(1)
[x + 24] =2[y - 24]............................(2), solve for x, y
We can solve this system of equations by substitution.
From the first equation, we have:
x - 5 = y + 5
Simplifying, we get:
x - y = 10
Solving for x in terms of y, we get:
x = y + 10
Now we can substitute this expression for x into the second equation:
x + 24 = 2(y - 24)
Substituting, we get:
(y + 10) + 24 = 2(y - 24)
Simplifying, we get:
y + 34 = 2y - 48
Subtracting y from both sides, we get:
34 = y - 48
Adding 48 to both sides, we get:
y = 82 - what your brother started with
Now that we know y = 82, we can substitute this value back into the first equation to solve for x:
x - y = 10
x - 82 = 10
Adding 82 to both sides, we get:
x = 92 - what you started with
So the solution to the system of equations is x = 92 and y = 82. Therefore, your brother currently has 82 dollars and if you give him 5 dollars, you both will have 87 dollars each. If he gives you 24 dollars, then you will have 116 dollars(or twice what he has), and he will have 58 dollars.
