Your school talent show allows people to sign up for 3 min. or 5 min. acts. There is 1 min. between acts. The talent show has 15 acts and lasts for 79 min. How many 3 minute acts are there?
If there are x 3-min acts and y 5-min acts, then you have 14 intermissions, so
x+y = 15
3x+5y+14=79
To solve this problem, we need to determine the number of 3-minute acts in the talent show.
Let's assume the number of 3-minute acts is "x".
Each 3-minute act takes 3 minutes to perform, and there is a 1-minute break between acts. So, each act, along with the break, takes a total of 4 minutes.
Since there are 15 acts in total, the total performance time, including breaks, is given by:
Total performance time = (Number of acts) x (Time per act + Break time)
In this case, the total performance time is 79 minutes, the number of acts is 15, the time per act is 3 minutes, and the break time is 1 minute.
Therefore, we can set up the equation:
79 = 15 x (3 + 1)
Now we can solve for "x" to find the number of 3-minute acts:
79 = 15 x 4
79 = 60 + 4x
4x = 79 - 60
4x = 19
x = 19/4
Since the number of acts must be a whole number, we need to round up to the nearest whole number.
Therefore, there are 5 three-minute acts in the talent show.