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# solve

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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 25 dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?

Jul 5, 2023

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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 25 dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?

Call M the original amount held by Me

Call B the original amount held by Brother

(M – 5)  =  (B + 5)               (eq 1)

(M + 25)  =  2 • (B – 25)      (eq 2)

Multiply (2) out                                        M + 25  =  2B – 50

Multiply both sides of (1) by 2               2M – 10  =  2B + 10

Subtract                                                –M + 35  =       – 60

Combine like terms                               –M           =       –95

Multiply both sides by –1                                 M  =  95

Plug value of M into (1)                             95 – 5  =  B + 5

Combine like terms                                         85  =  B

My Brother currently has 85 dollars

Plug 95 and 85 into (2)                            (95 + 25)  =  (2)(85 – 25)

120  =  2 • 60

120  =  120

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Jul 6, 2023