SOLUTION: Hello, I'm trying to help my 5th grader with a word problem, it's below, will much appreciate it , if you would help, got your site from google. This problem is due tom. morning.Th

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Question 165788: Hello, I'm trying to help my 5th grader with a word problem, it's below, will much appreciate it , if you would help, got your site from google. This problem is due tom. morning.Thank you

Ivan, Zoe, Denys and Ethan wanted to divided up a big old pickle 30 feet long.
Denys wants twice as much as Ivan does. Zoe wants twice as much as Denys does, but half as much as Ethan does.
How should they divide the pickle?
Found 3 solutions by vleith, Fombitz, Edwin McCravy:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let I be the amount Ivan wants.
Denys wants D+=+2I
Zoe wants Z+=+2D+=+2%2A%282I%29+=+4I
Zoe also wants Z=+E%2F2 so 4I+=+E%2F2 and 8I+=+E
Added up, they use the whole pickle
30+=+I+%2B+Z+%2B+D+%2B+E
30+=+I+%2B+4I+%2B+2I+%2B+8I
30+=+15I
2+=+I
If Ivan gets 2, then Denys gets 2*2 = 4
Zoe wants 4*I = 4*2 = 8
Ethan gets 8I (Ethan is a big pickle eater) - so E get 8*2 = 16

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's name everyone's cut length after the first letter of their name.
All their lengths together equal 30.
1.I%2BZ%2BD%2BE=30
"Denys wants twice as much as Ivan does"
2.D=2%2AI
"Zoe wants twice as much as Denys does"
3.Z=2%2AD=2%2A%282%2AI%29=4%2AI
"Zoe wants half as much as Ethan does"
4.Z=%281%2F2%29E
.
.
.
Since 3 and 4 both equal Z, set them equal to each other,
4%2AI=%281%2F2%29E
5.E=8%2AI
.
.
.
Now you can form an equation with only "I" as the variable, using substitutions from equations 2,3,and 5.
1.I%2BZ%2BD%2BE=30
I%2B%284%2AI%29%2B%282%2AI%29%2B%288%2AI%29=30
15%2AI=30
I=2
.
.
.
Now go back and substitute this value in each of the equations,
2.D=2%2AI=2%282%29=4
3.Z=4%2AI=4%282%29=8
5.E=8%2AI=8%282%29=16
.
.
.
Ivan gets 2 feet, Zoe gets 8 feet, Denys gets 4 feet and Ethan gets 16 feet.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Edwin's solution:

Ivan, Zoe, Denys and Ethan wanted to divided
 up a big old pickle 30 feet long. So,
I+%2B+Z+%2B+D+%2B+E+=+30

Denys wants twice as much as Ivan does. So,
D+=+2I

Zoe wants twice as much as Denys does
Z=+2D

Zoe wants...half as much as Ethan does. 

Z+=+%281%2F2%29E

So we have these equations:

I+%2B+Z+%2B+D+%2B+E+=+30
D+=+2I
Z=+2D
Z+=+%281%2F2%29E

Let's see if we can get equations for
I, D, and E in terms of Z. Then we'll substitute
them in the first equation.

From
Z+=+%281%2F2%29E, by multiplying both sides by 2,
2Z+=+E

So we have something to substitute for 
E in terms of Z, namely 2Z.

From 
Z=+2D, by multiplying both sides by 1%2F2,
%281%2F2%29Z=D

So we have something to substitute for 
D in terms of Z, namely %281%2F2%29Z.

From
D=2I, by mutiplying both sides by 1%2F2,
%281%2F2%29D=I.  Then we can substitute
%281%2F2%29Z for D in that, and get

%281%2F2%29%281%2F2%29Z=I which is the same as
%281%2F4%29Z=I

So we have something to substitute for 
I in terms of Z, namely %281%2F4%29Z.

So let's substitute all those in

I+%2B+Z+%2B+D+%2B+E+=+30, leaving Z as it is:

%281%2F4%29Z+%2B+Z+%2B+%281%2F2%29Z+%2B+2Z+=+30

Then we can multiply everything by 4 and get

Z+%2B+4Z+%2B+2Z+%2B+8Z+=+120

15Z=120

Then we can divide both sides by 15 and get

Z=8

Then we can get E from 
2Z+=+E
2%288%29=E
16=E

Then we can get D from

%281%2F2%29Z=D
%281%2F2%29%288%29+=+D
4=D

Finally we can get I from

%281%2F4%29Z=I
%281%2F4%29%288%29=I
2=I

So

Ivan gets 2 inches, Zoe gets 8 inches, 
Denys gets 4 inches, and Ethan gets 16 inches

Edwin