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avatar+952 

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)?

 Apr 3, 2024
 #1
avatar+128794 
+1

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

 

cool cool cool         

 Apr 3, 2024
edited by CPhill  Apr 4, 2024
 #2
avatar+2 
0

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

 Apr 4, 2024

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