How can we fairly distribute food among four people with different appetites?

  • Thread starter robax25
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  • #1
robax25
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Homework Statement
There are Four persons live in a room. At night, Someone gives them a lot of bread which can be counted. 1st Person eats 1/3 of the Food and put the rest in a basket after eating. 2nd person eats 1/3 of the food that was put in the basket by 1st person and he puts the rest in the basket after eating .3rd person eats 1/3 of the food that was put in the basket by 2nd person and he also puts food in the basket after eating .In the morning, they divide the food equally for three persons that was put in the basket by 3rd person at night. After dividing, there is a rest food that is eaten by 4th person what is called one Bred. how many Breads are there and How many breads are eaten by everyone? 4th person has eaten already 1. we need to find out for 3 persons.
Relevant Equations
sequence [a1], [a2] , [a3],[a4]----[an]
1st person consumes food =1/3=0.333. He puts in the basket = 1-1/3=0.666
2nd person consumes food=0.666/3=0.222 and He puts in the basket =0.666-.222=0.444
3rd person consumes food = 0.444/3=0.148 and he puts in the basket = 0.444-0.148=0.296

At morning, three persons consume food ,0.296/3=.098 means every one eats (.098/3)=.03 and 4th person consumes food =0.296-0.098=0.198
In total, 1st person consumes food =0.333+(.098/3)=0.366 =0.366/0.198=1.848~ 2 bread
In total, 2nd person consumes food =0.222+(.098/3)=0.255 =0.255/0.198=1.288~2bread
In total, 3rd person consumes food =0.148+(.098/3)=0.181 = 0.181/0.198=0.914~1 bread
4th person consumes food =0.198 ~1 bread

In total, there are 6 breads.
 
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  • #2
I suggest you work with fractions, rather than decimals. I assume that everyone eats a whole number of breads. If there were 6 breads, then the first person would eat 2 and put 4 back. But, now the second person cannot eat 1/3 of 4 breads. So, 6 breads is not right.
 
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  • #3
show me the right answer. I have confusion that how to calculate Morning's food that is eaten by each. Can you show me?
 
  • #4
If I consider that it is a sequence, then, I must follow the sequence. The three calculations can be calculated easily as they follow sequence. But the last one, there is a trick. If I follow the sequence, I must say that 0.198 is consumed by 4th person. The problem that, you cannot calculate that I eat 1.5 Bread, you must equal it. If you eat 1.2 bread , You must say 2 bread.
 
  • #5
It's against the rules to show you the answer, but I can tell you to use fractions (like ##\frac 1 3##) and not decimals (like 0.198), in this problem.
 
  • #6
PeroK said:
It's against the rules to show you the answer, but I can tell you to use fractions (like ##\frac 1 3##) and not decimals (like 0.198), in this problem.
1st person consumes food =1/3 He puts in the basket = 1-1/3=2/3

2nd person consumes food=(2/3)/3=2/9 and He puts in the basket =2/3-2/9=4/9

3rd person consumes food = (4/9)/3=4/27 and he puts in the basket = 4/9-4/27=8/27
At morning, three persons consume food ,(8/27)/3=8/81means every one eats (8/81)/3=8/243 and 4th person consumes food =8/27-8/81=16/81

In total, 1st person consumes food =(1/3)+(8/243)=89/243 =(89/243)/(16/81)=7209/3888=1.85~ 2 bread

In total, 2nd person consumes food =2/9+(8/243)=62/243= (62/243)/(16/81)=1.29~2bread

In total, 3rd person consumes food =4/27+(8/243)=44/243 = (44/243)/(16/81)=0.914~1 bread

4th person consumes food =16/81 ~1 bread
In total, there are 6 breads.
 
  • #7
robax25 said:
1st person consumes food =1/3=0.333. He puts in the basket = 1-1/3=0.666
2nd person consumes food=0.666/3=0.222 and He puts in the basket =0.666-.222=0.444
3rd person consumes food = 0.444/3=0.148 and he puts in the basket = 0.444-0.148=0.296

At morning, three persons consume food ,0.296/3=.098 means every one eats (.098/3)=.03
How can that be? Initially, the first person ate 1/3 of a larger amount than the second and third.
It is not clear that the amount divided in morning was eaten by persons 1, 2, and 3. Let's assume that is true.
I would start with a little algebra and represent the initial amount by x.
Initially, person 1 eats x/3 and passes 2x/3 on.
Initially, person 2 eats 2x/3 1/3 and passes on 2x/3 2/3.
etc.
See how far this takes you. Then set the amount eaten by person 4 to 1bread and solve for x.

PS. I completely agree with @PeroK that you should keep the fractions rather than decimals.
 
  • #8
If I consider for last calculation like that,
At morning, they divide the food, (8/27)/3=8/81. As there are 3 person, they eat more than one person.it means 3 person consume food at morning, 8/27- (8/81)=16/81 and rest 8/81. Then, the answer would be different.
 
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  • #9
FactChecker said:
How can that be? Initially, the first person ate 1/3 of a larger amount than the second and third.
It is not clear that the amount divided in morning was eaten by persons 1, 2, and 3. Let's assume that is true.
I would start with a little algebra and represent the initial amount by x.
Initially, person 1 eats x/3 and passes 2x/3 on.
Initially, person 2 eats 2x/3 1/3 and passes on 2x/3 2/3.
etc.
See how far this takes you. Then set the amount eaten by person 4 to 1bread and solve for x.

PS. I completely agree with @PeroK that you should keep the fractions rather than decimals.
it is clear that At morning they divide the rest food equally and After that, there is also rest food again and it is eaten by 4th person. 4th person eats food only at morning.
 
  • #10
how can be calculated the amount of food for 4th persons?
 
  • #11
robax25 said:
how can be calculated the amount of food for 4th persons?
Do you know what a remainder upon division is?
 
  • #12
robax25 said:
If I consider for last calculation like that,
At morning, they divide the food, (8/27)/3=8/81. As there are 3 person, they eat more than one person.it means 3 person consume food at morning, 8/27- (8/81)=16/81 and rest 8/81. Then, the answer would be different.
The total food is eaten by 1st person = 1/3+((16/81)/3)=97/243 means (97/243)/(8/81)=4 bread
The total food is eaten by 2nd person = 2/9+ ((16/81)/3)=70/243= means (70/243)/(8/81)=2.91~3
The total food is eaten by 3rdd person = 4/24 +((16/81)/3)=0.232 means 0.232/(8/81)=2.33~3
4th person is 1

in total 4+3+3+1=11 right?
PeroK said:
Do you know what a remainder upon division is?
Yes, i know. After dividing a number for example 10/3, here remainder is 1
 
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  • #13
robax25 said:
Yes, i know. After dividing a number for example 10/3, here remainder is 1
There's a remainder of 1 in this problem. That's all the 4th person gets in the morning.
 
  • #14
PeroK said:
There's a remainder of 1 in this problem. That's all the 4th person gets in the morning.
how does it is possible?. Because, the question is clearly state that the food is remained by 3rd person at night, In morning, the remained food they distribute it equally with 3 persons and the rest is given to 4th persons.
PeroK said:
There's a remainder of 1 in this problem. That's all the 4th person gets in the morning.
How do I calculate it?
 
  • #15
robax25 said:
how does it is possible?. Because, the question is clearly state that the food is remained by 3
They divide up the remaining food equally between 3, but one bread is left over for the 4th person. For example, if their were 7 breads left, they would take 2 each and leave 1.
robax25 said:
How do I calculate it?
Algebra!!
 
  • #16
Firstly, I think like that, you are right.

The total food is eaten by 1st person = 1/3+((16/81)/3)=97/243 means (97/243)/(8/81)=4 bread
The total food is eaten by 2nd person = 2/9+ ((16/81)/3)=70/243= means (70/243)/(8/81)=2.91~3
The total food is eaten by 3rdd person = 4/24 +((16/81)/3)=0.232 means 0.232/(8/81)=2.33~3
4th person is 1

in total 4+3+3+1=11 right?
 
  • #17
robax25 said:
Firstly, I think like that, you are right.

The total food is eaten by 1st person = 1/3+((16/81)/3)=97/243 means (97/243)/(8/81)=4 bread
The total food is eaten by 2nd person = 2/9+ ((16/81)/3)=70/243= means (70/243)/(8/81)=2.91~3
The total food is eaten by 3rdd person = 4/24 +((16/81)/3)=0.232 means 0.232/(8/81)=2.33~3
4th person is 1

in total 4+3+3+1=11 right?
I think you misunderstand the problem. The answer can't be 11, because you cannot take 1/3 of 11. The problem makes no sense unless we are calculating whole number of breads.
 
  • #18
where is the problem?
 
  • #19
robax25 said:
where is the problem?
11 is not divisble by 3. The first step is for the first person to eat 1/3 of the totals breads. 11 doesn't work.
 
  • #20
how does it work? because, after eating at night, the rest food is 8/27. In morning, I divide it by 3. it means
(8/27)/3=8/81 is for 4th person and 8/81*2=16/81 food is consumed by 3 persons at morning. Now if I consider 8/81 = 1 bread , then total food is consumed by one divides by (8/81), then I get the result.
 
  • #21
robax25 said:
how does it work? because, after eating at night, the rest food is 8/27. In morning, I divide it by 3. it means
(8/27)/3=8/81 is for 4th person and 8/81*2=16/81
No. They don't finish the food. They leave one bread for the fourth person. Remember the remainder.
 
  • #22
the reminder is 8/81
 
  • #23
robax25 said:
the reminder is 8/81
The remainder is 1.
 
  • #24
how?
 
  • #25
robax25 said:
how?
robax25 said:
.In the morning, they divide the food equally for three persons that was put in the basket by 3rd person at night. After dividing, there is a rest food that is eaten by 4th person what is called one Bred.
I interpret that to mean that one bread is left for the fourth person.
 
  • #26
if the result is 10 than 10/3 and 1 is remainder. 2.1 ~2 than the answer is right
 
  • #27
Firstly, I think like that, you are right.

The total food is eaten by 1st person = 1/3+((16/81)/3)=97/243 means (97/243)/(8/81)=4 bread
The total food is eaten by 2nd person = 2/9+ ((16/81)/3)=70/243= means (70/243)/(8/81)=2.91~3
The total food is eaten by 3rd person = 4/24 +((16/81)/3)=0.232 means 0.232/(8/81)=2.33~2
4th person is 1

now the answer is 4+3+2+1=10
 
  • #28
10 is right answer. am I right? because reminder is 1 now
 

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