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The singer Selena won a Billboard Latin Music Award for her song "Tú Sólo Tú." If there are 292 beats in 2 minutes of the song, which equation represents the proportional relationship between the number of beats, [tex]$b$[/tex], and the length of the song, [tex]$m$[/tex], in minutes?

A. [tex]$m = 146b$[/tex]
B. [tex][tex]$b = 146m$[/tex][/tex]
C. [tex]$m = 290b$[/tex]
D. [tex]$b = 290m$[/tex]


Sagot :

To determine the equation that represents the proportional relationship between the number of beats, [tex]\( b \)[/tex], and the length of the song, [tex]\( m \)[/tex], in minutes, let's break down the information given:

1. We know that there are 292 beats in 2 minutes of the song.
2. We need to find the relationship between beats and minutes.

Starting from the given data:
- There are [tex]\(292\)[/tex] beats for [tex]\(2\)[/tex] minutes.

First, let's calculate the number of beats per minute. We can do this by dividing the total number of beats by the total number of minutes:
[tex]\[ \text{beats per minute} = \frac{292 \text{ beats}}{2 \text{ minutes}} \][/tex]
[tex]\[ \text{beats per minute} = 146 \text{ beats per minute} \][/tex]

This tells us that for every minute, there are [tex]\(146\)[/tex] beats.

Next, we can express the relationship with an equation. Since the number of beats per minute is constant, the number of beats [tex]\( b \)[/tex] is directly proportional to the number of minutes [tex]\( m \)[/tex]. Therefore, we can write:

[tex]\[ b = 146m \][/tex]

This equation indicates that the number of beats [tex]\( b \)[/tex] is 146 times the number of minutes [tex]\( m \)[/tex].

Therefore, the correct equation representing the proportional relationship between the number of beats [tex]\( b \)[/tex] and the length of the song in minutes [tex]\( m \)[/tex] is:
[tex]\[ b = 146m \][/tex]
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