SOLUTION: Huey has four dollars more than two times as many dollars as Louie. Dewey has four fewer dollars than two times as many dollars as Huey. How much money does each have if the total

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Question 1090550: Huey has four dollars more than two times as many dollars as Louie. Dewey has four fewer dollars than two times as many dollars as Huey. How much money does each have if the total amount of money is 85?
Found 4 solutions by addingup, MathTherapy, josgarithmetic, greenestamps:
Answer by addingup(3677) About Me  (Show Source):
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H = 2L+4
D = 2L-4
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H + L + D = 85 substitute for H and D per above:
2L + 4 + L + 2L - 4 = 85
5L = 85
L = 17
So now we know how much Louie has Let's find Huey and Dewey:
H = 2L + 4; H = 2(17) + 4; H = 38
D = 2L - 4; D = 2(17) - 4; D = 30

Answer by MathTherapy(10552) About Me  (Show Source):
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Huey has four dollars more than two times as many dollars as Louie. Dewey has four fewer dollars than two times as many dollars as Huey. How much money does each have if the total amount of money is 85?
Correct answer: 

Let NO-ONE tell you otherwise! A few people on here are VERY GOOD at giving WRONG answers.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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Huey has four dollars more than two times as many dollars as Louie. Dewey has four fewer dollars than two times as many dollars as Huey.
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H, Huey
L, Louie
D, Dewey

system%28H=2L%2B4%2CD=2H-4%29

2L=H-4
L=H%2F2-2

In terms of H, same system is system%28L=H%2F2-2%2CD=2H-4%29.


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... if the total amount of money is 85
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H%2BL%2BD=85
H%2BH%2F2-2%2B2H-4=85
H%2BH%2F2%2B2H-6=85
3H%2BH%2F2=85%2B6
3H%2BH%2F2=91
6H%2BH=182
H=182%2F7
highlight%28H=26%29
Substitute for H=26 to find L and D.
-
highlight%28L=11%29
-
highlight%28D=48%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

You can also solve this using a single variable, instead of using three variables and solving a system of three equations. This can require a bit more time to set up the problem correctly; but once it is set up it often requires less time to reach the solution.

The given information compares Huey's amount to Louie's amount and then compares Dewey's amount to Huey's amount. So a good place to start is with Louie's amount.

Let x = Louie's amount
Then 2x+4 = Huey's amount (4 more than two times as much as Louie)
And 2(2x+4)-4 = 4x+4 = Dewey's amount (4 less than two times as much as Huey)

Then the total amount is 85, so
x+%2B+%282x%2B4%29+%2B+%284x%2B4%29+=+85
7x%2B8+=+85
7x+=+77

So Louie's amount is x = 11;
Huey's amount is 2x+4 = 22+4 = 26;
Dewey's amount is 4x+4 = 44+4 = 48.

It's always a good idea to make sure your answers are correct...
11+26+48 = 85... Good!!