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# Equations

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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)?

May 2, 2023

#1
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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)?

If I give my brother 5 dollars, then we will

have the same amount of money.                       Me – 5  =  Bro + 5

If instead he gives me 25 dollars, then I'll

have twice as much money as he will have.        Me + 25  =  2 * (Bro – 25)

By equation 1                           Me  =  (Bro + 10)

Substitute that value

for Me into equation 2              (Bro + 10) + 25  =  2Bro – 50

Bro + 35  =  2Bro – 50

85  =  Bro

That's the answer that was asked for; i.e., my brother has 85.

But continuing, just to be thorough, that means that I have 95.

If my brother gives me 25, then I'll have 120 and he'll have 60.

.

May 2, 2023
#2
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Here's what I think. Set my money to be m, and my brother's to be b.

System of equations:

m-5=b+5

\(m=b+10\)    (1)

(b-25)*2=m+25

\(m=2b-75\). (2)

Set (1) and (2) equal to get

\(2b-75=b+10\)

\(b=85\)

Which is the same thing guest got.

May 2, 2023