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(2517)   (Show Source):
You can put this solution on YOUR website!Let I be the amount Ivan wants.
Denys wants 
Zoe wants 
Zoe also wants  so  and 
Added up, they use the whole pickle
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(13823)  (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. 
"Denys wants twice as much as Ivan does"
2. 
"Zoe wants twice as much as Denys does"
3. 
"Zoe wants half as much as Ethan does"
4. 
.
.
.
Since 3 and 4 both equal Z, set them equal to each other,
5. 
.
.
.
Now you can form an equation with only "I" as the variable, using substitutions from equations 2,3,and 5.
1.
.
.
.
Now go back and substitute this value in each of the equations,
2. 
3. 
5. 
.
.
.
Ivan gets 2 feet, Zoe gets 8 feet, Denys gets 4 feet and Ethan gets 16 feet.
Answer by Edwin McCravy(6938)  (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,
Denys wants twice as much as Ivan does. So,
Zoe wants twice as much as Denys does
Zoe wants...half as much as Ethan does.
So we have these equations:
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
, by multiplying both sides by 2,
So we have something to substitute for
 in terms of Z, namely  .
From
, by multiplying both sides by  ,
So we have something to substitute for
 in terms of Z, namely  .
From
 , by mutiplying both sides by ,
 . Then we can substitute
for in that, and get
 which is the same as
So we have something to substitute for
 in terms of Z, namely  .
So let's substitute all those in
, leaving  as it is:
Then we can multiply everything by  and get
Then we can divide both sides by  and get
Then we can get E from
Then we can get D from
Finally we can get I from
So
Ivan gets 2 inches, Zoe gets 8 inches,
Denys gets 4 inches, and Ethan gets 16 inches
Edwin
|
|
|
