# 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. How many beats should there be in the second song?

Mar 25, 2018

$429$ beats

#### Explanation:

The number of beats is proportional to the time of the song.

Convert the time to seconds to avoid recurring decimals.

$4$ minutes $12$ seconds = $4 \times 60 + 12 = 252$ seconds

$3$ minutes $54$ seconds = $4 \times 60 - 6 = 234$ seconds

Set up a direct proportion using equivalent fractions:

x/234 = 462/252" "(larr"beats")/(larr"seconds")

$x = \frac{234 \times 462}{252}$

$x = 429$ beats