To find the day(s) when the attendance was the same at both plays, we can set the two equations equal to each other and solve for x:
15x + 76 = -x^2 + 36x - 4
x^2 + 21x - 80 = 0
(x + 25)(x - 4) = 0
x = -25 or x = 4
Since the number of days since opening night cannot be negative, the attendance was the same on day 4.
To find the attendance on day 4, we can substitute x = 4 into either equation:
Play A: y = 15(4) + 76 = 60 + 76 = 136
Play B: y = -4^2 + 36(4) - 4 = -16 + 144 - 4 = 124
Therefore, the attendance was the same on day 4, with a attendance of 136 at Play A and 124 at Play B.
The correct answer is: c. The attendance was the same on day 4. The attendance at both plays on that day was 136 and 124 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
a. The attendance was the same on day 5. The attendance was 151 at both plays on that day.
b. The attendance was the same on day 16. The attendance was 316 at both plays on that day.
c. The attendance was the same on days 5 and 16. The attendance at both plays on those days was 151 and 316 respectively.
d. The attendance was never the same at both plays.
1 answer