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 = 8x + 191
Play B: y = -x^2 + 26x + 126

a. The attendance was never the same at both plays.

b. The attendance was the same on day 5. The attendance was 231 at both plays on that day.

c. The attendance was the same on day 13. The attendance was 295 at both plays on that day.

d. The attendance was the same on days 5 and 13. The attendance at both plays on those days was 231 and 295 respectively.

Answer 1

Answer: option d is correct .

Step-by-step explanation:

In order to find the same attendance  we set both equation equal

8x+191 = -x^2+26x+126

simplifying equation ,we get

x^2 -18x+65=0

(x-5) (x-13) = 0

x =5  or x =13

therefore on 5th day and 13th day  both plays attendance  is same

and it is obtained by plugging x = 5 in  and x =13 in either of the equation.

for x = 5 ,

y = 8(5) +191 = 40+191 = 231

for x = 13

y = 8(13)+191

 = 104+191

 = 295

therefore option d is correct