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]: .$\displaystyle 7 + 10 + C \:=\:27 \quad\Rightarrow\quad \boxed{C \:=\:10}$

Re: Guess Who eats how much

you are good very good dude. Really

And plz can you tell what software is used?

Re: Guess Who eats how much

plz can you explain how m=4-5a/2 came?

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 $\displaystyle M=\frac{4-5a}{2}$

Re: Guess Who eats how much

Can we solve this Question in Matlab or begatrix?

Re: Guess Who eats how much

thanks to both of u espacially soroban

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.

Re: Guess Who eats how much