Since opening night, attendance at Play A has increased steadily, while attendance at Play B first rose and then fell. Equations modeling the daily attendance y at each play are shown below, where x is the number of days since opening night. On what day(s) was the attendance the same at both plays? What was the attendance?
Play A: y = 15x + 76
Play B: y = –x2 + 36x – 4(1 point)
Responses
The attendance was never the same at both plays.
The attendance was never the same at both plays.
The attendance was the same on day 16. The attendance was 316 at both plays on that day.
The attendance was the same on day 16. The attendance was 316 at both plays on that day.
The attendance was the same on days 5 and 16. The attendance at both plays on those days was 151 and 316, respectively.
The attendance was the same on days 5 and 16. The attendance at both plays on those days was 151 and 316, respectively.
The attendance was the same on day 5. The attendance was 151 at both plays on that day.
The correct answer is:
The attendance was the same on day 5. The attendance was 151 at both plays on that day.
To find this, you set the attendance equations for both plays equal to each other:
15x + 76 = -x^2 + 36x - 4
Solving for x, you get x = 5. Plugging x = 5 back into either equation gives y = 151. So, on day 5, the attendance was the same at both plays with 151 attendees.