SOLUTION: If I give my brother $8$ dollars, then we will have the same amount of money. If instead he gives me $19$ dollars, then I'll have twice as much money as he will have. How much mo

Question 1208627: If I give my brother $8$ dollars, then we will have the same amount of money. If instead he gives me $19$ dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?
Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

Answer: $73

Explanation

x = amount of money you start with
y = amount of money your brother starts with

Giving your brother $8 will decrease your amount to x-8.
Meanwhile his amount will increase to y+8.
At this point the two amounts are equal.
x-8 = y+8
x-8-8 = y
y = x-16
We'll substitute this into another equation.

If instead your brother gives you $19, then your amount increases to x+19 and his amount drops to y-19.
At this point your amount is twice that of his.
your amount = 2*(his amount)
x+19 = 2*(y-19)
x+19 = 2*(x-16-19) ....... plug in y = x-16
x+19 = 2*(x-35)
x+19 = 2x-70
x-2x = -70-19
-x = -89
x = 89 dollars is what you started with.

y = x-16
y = 89-16
y = 73 dollars is what your brother started with.

----------------------------
Check:

If you give him $8, then
your amount = 89-8 = 81 his amount = 73+8 = 81
Showing you both would end up with the same amount of money ($81)
This verifies the first condition.

If he gives you $19, then
your amount = 89+19 = 108 his amount = 73-19 = 54
Notice that 108 is twice that of 54
54*2 = 108
Both conditions have been verified.

Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

First do a little logical analysis to determine that the two of us will have the same amounts if I give him $8 means I start with $16 more than him. So

x = # of dollars he has to start
x+16 = # of dollars I start with

If he gives me $19, then

x-19 = # of dollars he will have
(x+16)+19 = x+35 = # of dollars I will have

In that case, I will have twice as much money as he will:

x+35 = 2(x-19)
x+35 = 2x-38
x = 73

ANSWER: He starts with $73

CHECK:
I start with x+16 = $89 and he starts with $73
If I give him $8, I will have $89-$8 = $81 and he will have $73+$8 = $81 -- same amounts
If he gives me $19, I will have x+35 = $108 and he will have $73-$19 = $54 -- I have twice as much as he has

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