Mr Wong bought a number of red, blue and green balloons. The ratio of the number of red balloons to the number of blue balloons to the number of green balloons was 15 : 12 : 28. After bursting some green balloons and buying another 168 blue balloons, he found that there was a decrease of $25\%$ in the total number of blue and green balloons. In the end, the number of red, blue and green balloons he had was 1440.

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
$320 = \text{Green burst} - 168$
$\text{Green burst} = 320 + 168 = 488$