黄先生买了一些红色、蓝色和绿色的气球。红色气球、蓝色气球和绿色气球的数量之比为 15 : 12 : 28。在一些绿色气球破裂并又买了 168 个蓝色气球之后，他发现蓝色 and 绿色气球的总数减少了 $25\%$。最终，他拥有的红色、蓝色和绿色气球的总数为 1440 个。

1. Express the initial number of balloons in terms of units.

Let the initial number of red, blue, and green balloons be $15u$, $12u$, and $28u$ respectively.
Total balloons at first = $15u + 12u + 28u = 55u$.

2. Find the final number of blue and green balloons in terms of units.

Initial total of blue and green balloons = $12u + 28u = 40u$.
Since there was a $25\%$ decrease, the final total of blue and green balloons is $100\% - 25\% = 75\%$ of the initial amount.
Final blue and green balloons = $\frac{75}{100} \times 40u = 30u$.

3. Form an equation using the final total number of balloons to find the value of 1 unit.

The number of red balloons remains unchanged at $15u$.
Total balloons in the end = $15u + 30u = 45u$.
Given that the final total is $1440$,
$45u = 1440$
$u = \frac{1440}{45} = 32$

4. Calculate the total number of balloons at first.

Total balloons at first = $55u = 55 \times 32 = 1760$.

1. Find the initial total number of blue and green balloons using the value of 1 unit from part (a)

From part (a), $1 \text{ unit} = 32$.
Initial blue balloons = $12 \times 32 = 384$
Initial green balloons = $28 \times 32 = 896$
Initial total of blue and green balloons = $384 + 896 = 1280$

2. Calculate the total decrease in blue and green balloons

Decrease = $25\%$ of $1280$
Decrease = $\frac{25}{100} \times 1280 = 320$

3. Use the net change to find the number of green balloons burst

The net decrease is the difference between the green balloons burst and the blue balloons bought.
Net decrease = Green burst $-$ Blue bought
$320 = \text{Green burst} - 168$
$\text{Green burst} = 320 + 168 = 488$