+1839 If I give my brother $5$ dollars, then we will have the same amount of money. If instead he gives me $10$ dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?
+129852 M - 5 = B + 5 → M = B + 10 (1)
M + 10 = 2 ( B - 10)
M + 10 = 2B - 20
M = 2B - 30 (2)
Set (1) = (2)
B + 10 = 2B -30
40 = B
Your brother has $40
Check
Your brother has 40 , you have 50
When you give him 5, he has 45, you have 45
Instead, when he gives you 10 , he has 30 and you have 60
+2 Let x be the number of dollars my brother has. Since we will have the same amount of money if I give him 5 dollars, I must have x + 10 dollars. (Make sure you see why I don't have x + 5 dollars. If I give him 5 dollars of my x + 10 dollars, then we will both have x + 5 dollars.)
If he gives me 17 dollars, then he will have x - 17 dollars and I will have x + 10 + 17 = x + 27 dollars. I'll then have twice as much money as he has, so
x + 27 = 2(x - 17) Expanding the right-hand side gives x + 27 = 2x - 34, so x = 61. So, my brother has $61, and I have $71
