Question

Can someone check my answer? Also show you work so I know you didn't choose a random answer. I Pick C for the following problem:

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

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.

Answer 1

set both equations equal:
15x + 76 = –x2 + 36x – 4
x^2-21x+80=0
(x-5)(x-16)=0
x=5, and x=16
attendance at x=16 ...since you already know attendance was the same on day 5 and 16, you dont need to check attendance with both formulas
attendance16= 15*16+76=240+76=316
attendance5= 15*5+76=151

Answer 2

Thank you so much!

Just checking because I'm stupid. C is correct yes?