Answer:
Let's denote the number of chocolates in the box as \(x\).
According to the given ratio, Bryn receives \(5\) parts and Carys receives \(4\) parts. So, the total number of parts is \(5 + 4 = 9\).
Thus, Bryn receives \(\frac{5}{9}\) of the chocolates, and Carys receives \(\frac{4}{9}\) of the chocolates.
We can set up the equation based on the ratio of the chocolates they receive:
\[Bryn's \ share = \frac{5}{9}x\]
\[Carys' \ share = \frac{4}{9}x\]
Since there are no chocolates remaining, the total number of chocolates is distributed completely:
\[Bryn's \ share + Carys' \ share = x\]
Substituting the values:
\[\frac{5}{9}x + \frac{4}{9}x = x\]
Now, let's solve for \(x\):
\[\frac{5}{9}x + \frac{4}{9}x = x\]
\[\frac{9}{9}x = x\]
\[x = \text{Total number of chocolates}\]
So, the total number of chocolates in the box must be divisible by \(9\), as it needs to be distributed among Bryn and Carys in nine equal parts.
Now, since the number of chocolates must be between \(20\) and \(30\), the only possible value satisfying both conditions is \(27\).
Thus, there were originally \(27\) chocolates in the box.
