Answer :
To determine the correct equation for the verbal sentence: "The ticket price, [tex]\( t \)[/tex], for a concert attended by 220 people equals the total revenue, [tex]\( r \)[/tex], divided by the number of people who attended," let's break down the information step-by-step.
1. The total revenue from the concert is represented by [tex]\( r \)[/tex].
2. This revenue is generated by selling tickets.
3. Each of the 220 people attending the concert has purchased a ticket.
4. The ticket price, [tex]\( t \)[/tex], is the total revenue [tex]\( r \)[/tex] divided by the number of attendees (220 people).
So, we need to express the ticket price [tex]\( t \)[/tex] in terms of the total revenue [tex]\( r \)[/tex] and the number of attendees (220 people). This relationship is mathematically stated as:
[tex]\[ t = \frac{r}{220} \][/tex]
Now, let's evaluate the given options:
a. [tex]\( t = \frac{r}{220} \)[/tex] - This correctly represents [tex]\( t \)[/tex] as the total revenue [tex]\( r \)[/tex] divided by the number of people (220).
b. [tex]\( t = 220 - r \)[/tex] - This incorrectly subtracts the total revenue [tex]\( r \)[/tex] from 220, which doesn’t match the description.
c. [tex]\( t = 220r \)[/tex] - This incorrectly multiplies the total revenue [tex]\( r \)[/tex] by 220, which doesn’t match the description.
d. [tex]\( t = 220 + r \)[/tex] - This incorrectly adds the total revenue [tex]\( r \)[/tex] to 220, which doesn’t match the description.
Therefore, the best answer is:
[tex]\[ A. \ t = \frac{r}{220} \][/tex]
1. The total revenue from the concert is represented by [tex]\( r \)[/tex].
2. This revenue is generated by selling tickets.
3. Each of the 220 people attending the concert has purchased a ticket.
4. The ticket price, [tex]\( t \)[/tex], is the total revenue [tex]\( r \)[/tex] divided by the number of attendees (220 people).
So, we need to express the ticket price [tex]\( t \)[/tex] in terms of the total revenue [tex]\( r \)[/tex] and the number of attendees (220 people). This relationship is mathematically stated as:
[tex]\[ t = \frac{r}{220} \][/tex]
Now, let's evaluate the given options:
a. [tex]\( t = \frac{r}{220} \)[/tex] - This correctly represents [tex]\( t \)[/tex] as the total revenue [tex]\( r \)[/tex] divided by the number of people (220).
b. [tex]\( t = 220 - r \)[/tex] - This incorrectly subtracts the total revenue [tex]\( r \)[/tex] from 220, which doesn’t match the description.
c. [tex]\( t = 220r \)[/tex] - This incorrectly multiplies the total revenue [tex]\( r \)[/tex] by 220, which doesn’t match the description.
d. [tex]\( t = 220 + r \)[/tex] - This incorrectly adds the total revenue [tex]\( r \)[/tex] to 220, which doesn’t match the description.
Therefore, the best answer is:
[tex]\[ A. \ t = \frac{r}{220} \][/tex]