With only two linear cuts, it is possible to divide the chocolate cue represented as a matrix of rows 4 and columns 5 so that Aldo gets half, Bruno a fifth, to Ciro the remaining part.
How much does Ciro get as a fraction?
Answer this last question in two ways: either by deducting it from the figure based on the cuts made, or by calculating an an appropriate numerical expression.
The chocolate cue is represented as a matrix of 4 rows and 5 columns:
$$ \begin{bmatrix} X & X & X & X & X \\ X & X & X & X & X \\ X & X & X & X & X \\ X & X & X & X & X \end{bmatrix} $$ We cut the chocolate stick in half along the lines:
$$\begin{bmatrix} X & X & X & X & X \\ X & X & X & X & X \end{bmatrix} $$
$$\begin{bmatrix} X & X & X & X & X \\ X & X & X & X & X \end{bmatrix} $$ Aldo gets the upper half.
We cut the bottom half in half along the columns:
$$ \begin{bmatrix} X & X \\ X & X \end{bmatrix} $$
Aldo gets the top half, Bruno gets the piece on the left, and Ciro gets the piece on the right.
If we denote the total number of chocolate squares as $N$, we have:
- Aldo gets $\frac{1}{2}N$.
- Bruno gets $\frac{1}{5} \times \frac{1}{2}N = \frac{1}{10}N $.
- Ciro gets $\frac{4}{5} \times \frac{1}{2}N = \frac{2}{5}N $.
The sum of these quantities must equal the total, so:
$$ \frac{1}{2}N + \frac{1}{10}N + \frac{2}{5}N = N $$
$$\frac{1}{2} + \frac{1}{10} + \frac{2}{5} = 1 $$
Cyrus gets $\frac{2}{5}$ of the chocolate stick but the solution is $3/10$.
Bruno gets a fifth of the entire chocolate bar, not a fifth of the remaining half after Aldo gets his half. So Aldo gets $N/2$, Bruno gets $N/5$ and Ciro the rest. Can you take it from here?