Question

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? which is the true correct answer and why

Play A: y = 15x + 76

Play B: y = –x2 + 36x – 4
(1 point)
Responses

The attendance was the same on day 5. The attendance was 151 at both plays on that day.
The attendance was the same on day 5. The attendance was 151 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 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 never the same at both plays.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct answer is:

The attendance was the same on day 5. The attendance was 151 at both plays on that day.

To find the point at which the attendance is the same at both plays, we need to set the two equations equal to each other and solve for x:
15x + 76 = -x^2 + 36x - 4
x^2 - 21x + 80 = 0
(x - 5)(x - 16) = 0
x = 5 or x = 16

Since day 5 comes before day 16, the attendance is the same on day 5 at both plays. Substituting x = 5 into either equation, we get:
Play A: y = 15(5) + 76 = 151
Play B: y = -(5)^2 + 36(5) - 4 = 151

Therefore, the attendance was 151 at both plays on day 5.