Step-by-step explanation:
Let the number of singing act be x
Let the number of comedy act be y
If the total act is 14, then;
x+y = 14..... 1
If singing acts are 4.5 minutes long and comedy acts are 3.5 minutes long and the acts lasts 59 minutes, then:
4.5x + 3.5y = 59 .......... 2
Solve both equation simultaneously for x and y
x+y = 14
45x+35y = 590
.................................
x+y = 14......... *9
9x+7y = 118....... 1
...............................
9x+9y = 126
9x+7y = 118
Subtract both equations
9y-7y = 126-118
2y = 8
y = 8/2
y = 4
Substitute y = 4 into equation 1;
From 1: x+y = 14
x+4 = 14
x = 14-4
x =10
Hence there are 10 singing acts and 4 comedy acts in the show
