# math logic problem??

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• Oct 14th 2007, 06:20 PM
anime_mania
math logic problem??
there are 100 loaves of bread to be passed out to 100 people. a child would get half, a lady would get 2 loaves and a man would get 3? how many children, women, and men are in the town if all the bread is passes out.

7 possible answers

thanks
• Oct 14th 2007, 06:29 PM
ffezz
oops my bad one sec
• Oct 14th 2007, 07:08 PM
cozi
Is there any other information in the question.
Hi anime_mania,

Is there any constraint on the ratio of number of children, ladies and men?

Here are just some solutions, without constraints, it worked out to be more than 7 solutions.

1. Try to fit as much males as possible
100/3 = 33 and 1/3 , where 1 male takes 3 loaves
=> 33 men and left with 1 loaf of bread.
1 loaf can be given to 2 children.

Therefore, 33 men, 2 children and zero ladies

2. Try to fit as many ladies a possible
100/2 = 50, where 1 lady takes 2 loaves
=> 50 ladies, zero male, zero child

3. Try to fit as all children
100/(1/2) = 200 children, where 1 children takes half a loaf
=> 200 children, zero male, zero female

4. Try to fit with an even distribution
Let a group be 1 male, 1 lady and 1 children.
Loaves of bread required for a group is 3 + 2 + 0.5 = 5.5
100/5.5 = 18.181818....

18 * 5.5 = 99
=> we can have 18 groups with 1 loaf of bread left (100 - 99)
1 loaf can be distributed to 2 children

Therefore, we can have
18 males, 18 ladies and 20 children.

5. From solution 4. Decrease the number of males to 17, distribute to 1 more lady and 2 children. You will have
17 males, 19 ladies and 22 children.

6. From solution 4. Decrease the number of male to 17, distribute all to 6 children
17 males, 18 ladies and 26 children.

7. From solution 4. Decrease the number of ladies to 17, distribute all to 4 children
18 males, 17 ladies and 24 children.

You can go on and on adjusting the number with different combination.

For every male that you reduce (3 loaves of bread available), you can either add 1 lady (2 loaves each lady) and 2 children (1/2 loaf each child) or zero lady and 6 children (1/2 loaf each child).

For every lady that you reduce (2 loaves of bread available), you can add 4 children (1/2 loaf each child).

For every 2 ladies that you reduce (4 loaves of bread available), you can add 1 male (3 loaves of bread) and 2 children (1/2 loaf each child).

You will end up with more than 7 solutions.

Regards,
cozi.

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