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?

Question

Play A: y = 15x + 76
Play B: y=-x+ 36x-4
(1 point)
The attendance was the
O same on day 5. The
attendance was 151 at both plays on that day.
The attendance was the
O same on day 16. Ine attendance was 316 at both plays on that day.
The attendance was the same on days 5 and 16.
• The attendance at both plays on those days was 151 and 316 respectively.

Answer 1

To find the day(s) when the attendance was the same at both plays, we need to set the two equations equal to each other and solve for x:

15x + 76 = -x + 36x - 4
Combine like terms:
16x + 76 = 36x - 4
Add x to both sides:
17x + 76 = 36x - 4
Add 4 to both sides:
17x + 80 = 36x
Subtract 17x from both sides:
80 = 19x
Divide by 19:
x = 80/19
x ≈ 4.21

Since x represents the number of days since opening night, we can't have a fraction of a day. The attendance was the same on the nearest whole number day, which is day 4. The attendance on day 4 can be found by plugging x = 4 into either equation:

Play A: y = 15(4) + 76 = 60 + 76 = 136 attendees
Play B: y = -(4) + 36(4) - 4 = -4 + 144 - 4 = 136 attendees

Therefore, the attendance was the same at both plays on day 4, with 136 attendees.