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=25x+136
Play B: y=-x^2+44x+76

Answer 1

Answer: Day 4 and 15

Explanation:

Set up system of equations:

`25x+136=-x^2+44x+76`

Simplify:

`x^2-19x+60=0`

Factor: Both factors must be positive as the days can only be natural numbers.

`(x-15)(x-4)=0`

x=4,15