Question

Two musicals that had very long Broadway runs were A Chorus Line and Beauty and the Beast. During their runs, there were 676 fewer performances of Beauty and the Beast than of A Chorus Line. The two shows had a total of 11,598 performances. a.Write a system of equations to represent this scenario. Be sure to define your variables!b.Calculate how many performances there were of each show by solving your system of equations.

Answer 1

let y = A Chorus Line; and x = Beauty and the Beast.

x = y - 676 (1)

x + y = 11598 (2)

We can solve the system by equaling both equations, as follows:

x = y - 676 (1)

x = 11598 - y (2)

y - 676 = 11598 - y

2y = 11598 + 676

2y = 12274

y = 6137 performances of A Chorus Line.

Now we substitute the y value on any of both equations:

x = 6137 - 676

x = 5461 performances of Beauty and The Beast