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 × 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

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 × is the number of days since opening night. On what day(s) was the attendance the same at both plays? What was the attendance?

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:

For Play A: y = 50 + 10x
For Play B: y = 80 - 5x

Setting them equal to each other:
50 + 10x = 80 - 5x
15x = 30
x = 2

So, on day 2, the attendance was the same at both plays. To find the attendance, we can substitute x = 2 into either equation:

For Play A: y = 50 + 10(2) = 50 + 20 = 70
For Play B: y = 80 - 5(2) = 80 - 10 = 70

Therefore, on day 2, the attendance was 70 at both Play A and Play B.