Question

A band's first song is 4 minutes, 12 seconds long and has 462 beats.

The band wants to have a second song that is 3 minutes, 54 seconds long with the same beats per minute as the first song.

There would be
??
total beats in the second song.

Answer 1

4 minutes 12 seconds is 252 seconds
3 minutes 54 seconds is 234 seconds

252 seconds for 462 beats is in proportion with 234 seconds with some number of beats
`x`

Set up the proportion:

`(252)/(462)=(234)/(x)`
⇒
`252x=234*462`
⇒
`252x=108108`
⇒
`x=429`

So the new song has 429 beats.