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# help I have no idea

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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
+129829
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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

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

Apr 3, 2024
edited by CPhill  Apr 4, 2024
#2
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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