Amil、Bala 和 Charles 拥有的钱数之比为 8 : 3 : 5。在他们每个人都花掉了相同数量的钱后，Amil 还剩下 $66。Charles 剩下的钱是 Bala 剩下钱的 5 倍。求这 3 个孩子起初拥有的钱的总数。 答案 : $ ___

1. Identify the constant difference between Charles's and Bala's money

Since Charles and Bala spent the same amount of money, the difference between their amounts remains constant.
Initial difference in units = $5\text{ units} - 3\text{ units} = 2\text{ units}$.

2. Relate the final ratio to the initial units using the constant difference

In the end, Charles had 5 times as much as Bala, so the final ratio is $C : B = 5 : 1$.
Final difference in parts = $5\text{ parts} - 1\text{ part} = 4\text{ parts}$.
Equating the differences: $4\text{ parts} = 2\text{ units}$, which means $1\text{ part} = 0.5\text{ units}$.
So, Bala had $0.5\text{ units}$ left.

3. Find the amount spent by each child in terms of units

Amount spent by Bala = Initial amount - Final amount = $3\text{ units} - 0.5\text{ units} = 2.5\text{ units}$.
Since they all spent the same amount, Amil and Charles also spent $2.5\text{ units}$ each.

4. Find the value of 1 unit using Amil's remaining money

Amil's remaining money = $8\text{ units} - 2.5\text{ units} = 5.5\text{ units}$.
We are given that Amil had $\char36{}66$ left.
$5.5\text{ units} = \char36{}66$
$1\text{ unit} = \char36{}66 \div 5.5 = \char36{}12$

5. Calculate the total amount of money at first

Total initial units = $8 + 3 + 5 = 16\text{ units}$.
Total amount at first = $16 \times \char36{}12 = \char36{}192$.