## Task B-1.3.

Each member of Marića's family drank 4 deciliters of a coffee and milk mixture. The amount of coffee and milk is different in each cup, but it is never zero. Marića drank one quarter of the total amount of milk and one sixth of the total amount of coffee. How many members are there in Marića's family?
## Solution.

Let $k$ be the amount of coffee, and $m$ be the amount of milk that Marica drank (in dl). Let the family have $n$ members. Since each member of the family drank $4 \mathrm{dl}$ of the coffee and milk mixture, a total of $4 n$ of the mixture was consumed, so the following equations hold:

$$
\begin{aligned}
& k+m=4 \\
& 6 k+4 m=4 n \\
& k>0, m>0, n \in \mathbb{N}
\end{aligned}
$$

Determine $k$ and $m$ in terms of $n$.

$$
\begin{aligned}
& m=4-k \\
& 6 k+4(4-k)=4 n \\
& k=2 n-8 \\
& m=12-2 n
\end{aligned}
$$

Since the amount of coffee and milk cannot be 0, for the numbers $k$ and $m$ it holds that:

$$
2 n-8>0 \text { and } 12-2 n>0
$$

It follows that $n>4$ and $n<6$, so $n=5$.

Marica's family has 5 members.