can someone please help me solve this problem?

Question

The halftime period at a football game is 30 min long. The cheerleaders have to perform before and after the band; however, the band plays 5 min longer than the cheerleaders dance. How long does each group perform?

I am thinking the cheerleaders performed for 10 minutes and the band performed for 20 minutes. Am I correct?

Answer 1

Not quite.
The cheerleaders have to perform before and after the band, that makes 10+20+10=40 minutes, and 20≠10+5.

Let the time for each dance be D.

"the band plays 5 min longer than the cheerleaders dance."
Band = D+5 minutes.

"The halftime period at a football game is 30 min long." and
"The cheerleaders have to perform before and after the band":

D + (D+5) + D = 30

Solve for D.

Answer 2

Is it D + (D+5)+ D = 30
5 + (15+5) + D = 30
5 + 20 + 5 = 30

Answer 3

Let's try it this way:
D + (D+5) + D = 30
D+D+D+5 = 30
3D+5 -5 = 30 -5
3D = 25
D=25/3=8 1/3 minutes

Check:
dance: 2 times 8 1/3 = 16 2/3 minutes
band: 8 1/3 + 5 = 13 1/3 minutes
Total = 16 2/3 + 13 1/3 = 30 minutes