Question 1209045: If I give my brother $5$ dollars, then we will have the same amount of money. If instead he gives me $12$ dollars, then I'll have four times as much money as he will have. How much money does my brother currently have (in dollars)?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Answer: $23.33
Explanation
x = amount of money you start with
y = amount of money your brother starts with
Scenarion 1) You give your brother $5
Scenarion 2) Your brother gives you $12
| Your amount | Your brother's amount | | Scenario 1 | x-5 | y+5 | | Scenario 2 | x+12 | y-12 |
At the conclusion of scenario 1, the two of you have the same amount of money.
your amount = his amount
x-5 = y+5
y = x-5-5
y = x-10
We'll use this equation later in a substitution step.
At the conclusion of scenario 2, you have four times as much money compared to your brother.
your amount = 4*(his amount)
x+12 = 4*(y-12)
x+12 = 4*(y-12)
x+12 = 4*(x-10-12) .... substitution
x+12 = 4(x-22)
x+12 = 4x-88
x-4x = -88-12
-3x = -100
x = -100/(-3)
x = 100/3
x = 33.33 dollars approximately
y = x-10 = 33.33 - 10 = 23.33 dollars is the amount your brother starts with.
Check:
| Your amount | Your brother's amount | | Scenario 1 | 33.33-5 = 28.33 | 23.33+5 = 28.33 | | Scenario 2 | 33.33+12 = 45.33 | 23.33-12 = 11.33 |
45.33/11.33 = 4.000882612533 approximately
We don't land on 4 exactly, but we get close enough.
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
If I give my brother $5$ dollars, then we will have the same amount of money. If instead he gives me
$12$ dollars, then I'll have four times as much money as he will have. How much money does my brother
currently have (in dollars)?
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As worded, printed, posted and presented, this problem is mathematically FATALLY DEFECTIVE,
since it has no a precise solution in integer number of cents.
In such problems, their meaning ALLWAYS assumes a precise solution; approximate solutions
with non-integer number of cents are not appropriate, are not accepted and can not be accepted.
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