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Question 1197384: There are three cousins who want to pool their money. Huey has d dollars. Louie has half of Huey's money. Dewey has 3 fewer dollars than Huey. If the sum of their money is $122, how much does each cousin have?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
After reading the problem, we write this
H + L + D = 122 dollars.
Then we replace L with H/2 and replace D with (H-3) - - - the reasons why we do it are clear.
Then the equation takes form
H + H/2 + (H-3) = 122.
Next you multiply everything by 2 and simplify step by step
2H + H + 2H - 6 = 244
5H = 250
H = 250/5 = 50.
Thus we learned that Huey has 50 dollars.
From this point, complete the rest on your own.
Solved, with pretty full explanations.
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
The response from the other tutor shows one good standard formal algebraic solution.
If a formal algebraic solution is not required, the problem can be solved quickly and easily using logical reasoning and simple arithmetic.
Note that, even if you are asked for a formal algebraic solution, you can get good brain exercise and good practice in problem solving working the problem that way.
(1) Give Dewey $3 more, so that he and Huey now have the same amount, and the total is now $125.
(2) Louie now has half as much as each of the others, so the total is now 2.5 times the amount each of Huey and Dewey have.
(3) So the total $125 is 2.5 times the amount each of Huey and Dewey have; that means the amount each of them has is $125/2.5 = $50.
(4) Then take away the extra $3 you gave to Dewey.
ANSWERS: The amounts each of them has are
Huey: $50
Dewey: $50-$3 = $47
Louie: $50/2 = $25
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