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)
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.

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? 
Play A: y = 15x + 76 
Play B: y = –x2 + 36x – 4 (1 point)
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.

whpalmer4 · Answer

To find the day where attendance was the same, set the equations equal to each other and solve for $x$:
$$15x+76=-x^2+36x-4$$$$x^2-21x+80=0$$This equation has two solutions because of the $x^2$ term.  Having found your values of $x$, plug them into one of the formulas to find the attendance on that day.