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

Answer 1

To find the day(s) when the attendance was the same at both plays, we need to set up the equation:

15x + 76 = -x^2 + 36x - 4.

Now, we can rearrange this equation to set it equal to zero:

x^2 + 21x - 80 = 0.

Now we can solve this quadratic equation by factoring or using the quadratic formula. Factoring gives:

(x + 25)(x - 4) = 0.

Setting each factor equal to zero gives x = -25 or x = 4.

Since we are asked for the number of days since opening night, we discard the negative solution and consider x = 4.

Therefore, on the 4th day since opening night, the attendance was the same at both plays. To find the attendance for that day, we can substitute x = 4 into either equation. Using Play A's equation:

y = 15(4) + 76
y = 60 + 76
y = 136.

Therefore, on the 4th day, the attendance at both Play A and Play B was 136.