To find the day(s) when the attendance was 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
This simplifies to:
x^2 - 21x + 80 = 0
Factoring this quadratic equation, we get:
(x - 5)(x - 16) = 0
So, x = 5 or x = 16.
Therefore, the attendance was the same on day 5 and day 16.
Plugging in x=5 into either equation:
y = 15(5) + 76 = 151
Therefore, the attendance at both plays on day 5 was 151.
Plugging in x=16:
y = 15(16) + 76 = 316
Therefore, the attendance at both plays on day 16 was 316.
Therefore, the correct answer is:
The attendance was the same on days 5 and 16. The attendance at both plays on those days was 151 and 316 respectively.
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 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 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.
1 answer