The100th blow was the100th minute, because all the soap bubbles burst in 2.5 minutes. From the first100th minute, only the 98th, 99th and100th blows are still within the time range. However, the previous 97 times were all two and a half minutes longer than the current time, and they were all broken, so they don't need to be considered. Just watch 98, 99, 100 times.

The 98th time, two minutes later, 100*( 1/20)=5.

The 99th time, one minute passed, 100*( 1/2)=20.

100， 100

5+50+ 100= 155

Attached:

1, 99 minutes have passed for the hundredth time, and it's all broken.

The second blow, the hundredth time has passed 98 minutes, all broken.

……

It's been blown for the 97th time, and it's been 3 minutes since the100th time, and it's all broken.

It's been two minutes since the 98th strike. 1/20 hasn't been broken yet, and there are 5 left.

The 99th strike, 1 minute has passed. The 99th strike, 100, 1/2 is broken, leaving 50.

Get 100 for the first time, 100+50+5 =155.