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=-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.
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.