can someone please help me solve this problem?
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?
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.
Is it D + (D+5)+ D = 30
5 + (15+5) + D = 30
5 + 20 + 5 = 30
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
To solve this problem, we can set up equations based on the given information. Let's denote the time the cheerleaders perform as "x" minutes.
According to the problem, the band plays 5 minutes longer than the cheerleaders, so the band's performance time would be "x + 5" minutes.
The total halftime period is 30 minutes, so the sum of the cheerleaders' and band's performance times should be equal to 30 minutes.
Therefore, we can write the equation:
x + (x + 5) = 30
Simplifying the equation:
2x + 5 = 30
2x = 30 - 5
2x = 25
x = 25/2
x = 12.5
So, the cheerleaders perform for 12.5 minutes and the band performs for 12.5 + 5 = 17.5 minutes.
Therefore, your answer is incorrect. The cheerleaders performed for 12.5 minutes, and the band performed for 17.5 minutes.