Answer:
3500
Step-by-step explanation:
The first show attendance was 3000 -2580 = 420 short of the desired average.
The second show attendance was 3000 -2920 = 80 short of the desired average.
In order for the average to be 3000, the attendance at the third show must exceed the desired average by an amount that makes up for the shortfall:
420 +80 = 500
Attendance at the 3rd show must be 3000 +500 = 3500.
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Alternate solution
You can also attack this problem in the conventional way: use a variable (x) for the required attendance and write the equation of the average.
(2580 +2920 +x)/3 = 3000 . . . . . . the average is the sum divided by 3
5500 +x = 9000 . . . . . . . . . . . . . . . multiply by 3
x = 3500 . . . . . . . . . . . . . . . . . . . . . . subtract 5500
3500 must attend the third show to bring the average up to 3000.
