# Guess Who eats how much

• Apr 26th 2013, 08:04 PM
Zshan96
Guess Who eats how much
Hello dear! how are you all hope be finei was asked a puzzle plz solve itIn a house there live 27 people and 1 man eats 4 bread and a woman eats 3 bread and a child eats half. every day 63 bread is eaten tell me how many man, woman and child are living in that house?plz solve it as soon as possible
• Apr 27th 2013, 04:48 PM
Soroban
Re: Guess Who eats how much
Hello, Zshan96!

Quote:

In a house there live 27 people.
One man eats 4 bread, a woman eats 3 bread, and a child eats half a bread.
Every day 63 breads are eaten.
How many men, women and children are living in that house?

Let: .$\displaystyle \begin{Bmatrix}M &=& \text{no. of men} \\ W &=& \text{no. of women} \\ C &=& \text{no. of children} \end{Bmatrix}$

We have: .$\displaystyle M+W+C \:=\:27\;\;[1]$

And: .$\displaystyle 4M + 3W + \tfrac{1}{2}C \:=\:63 \quad\Rightarrow\quad 8M + 6W + C \:=\:126\;\;[2]$

Subtract [2] - [1]: .$\displaystyle 7M + 5W \:=\:99$

. . $\displaystyle W \:=\:\frac{99-7M}{5} \quad\Rightarrow\quad W \:=\:19 - M + \frac{4-2M}{5}\;\;[3]$

Since $\displaystyle W$ is an integer, $\displaystyle 4-2M$ must be a multiple of 5.

That is: .$\displaystyle 4-2M \:=\:5a$, for some integer $\displaystyle a.$

. . $\displaystyle M \:=\:\frac{4-5a}{2} \quad\Rightarrow\quad M \:=\:2 - 2a - \tfrac{a}{2}\;\;[4]$

Since $\displaystyle M$ is a positive integer, $\displaystyle a$ must be a negative even number.
The first time this happens is: .$\displaystyle a = \text{-}2$

Substitute into [4]: .$\displaystyle M \:=\:2 - 2(\text{-}2) - \frac{\text{-}2}{2} \quad\Rightarrow\quad \boxed{M \:=\:7}$

Substitute into [3]: .$\displaystyle W \:=\:19 -7 + \frac{4-14}{5} \quad\Rightarrow\quad \boxed{W \:=\:10}$

Substitute into [1]: .$\displaystyle 7 + 10 + C \:=\:27 \quad\Rightarrow\quad \boxed{C \:=\:10}$
• Apr 27th 2013, 10:37 PM
Zshan96
Re: Guess Who eats how much
you are good very good dude. Really
And plz can you tell what software is used?
• Apr 27th 2013, 10:43 PM
Zshan96
Re: Guess Who eats how much
plz can you explain how m=4-5a/2 came?
• Apr 27th 2013, 11:55 PM
Shakarri
Re: Guess Who eats how much
It comes from
$\displaystyle W=19-M+\frac{4-2M}{5}$
W can't be a fraction because you can't have half a man. If W is not a fraction then $\displaystyle \frac{4-2M}{5}$ is not a fraction which can only be true if the top is divisible by 5.
If the top is divisible by 5 then it is equal to some number 'a' times 5 so $\displaystyle 4-2M=5a$. Rearrange for M $\displaystyle M=\frac{4-5a}{2}$
• Apr 28th 2013, 09:31 AM
Zshan96
Re: Guess Who eats how much
Can we solve this Question in Matlab or begatrix?
• Apr 29th 2013, 02:41 AM
Zshan96
Re: Guess Who eats how much
thanks to both of u espacially soroban
• May 1st 2013, 03:24 AM
Zshan96
Re: Guess Who eats how much
last thin that confusing me that how can we say that a=-2 plz explain how can -a/2 =a=-2 plz explain further plz.
• Jul 18th 2013, 11:20 PM
DVDHD
Re: Guess Who eats how much
Oh, I also want to know.

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