There are 7 groups of five and 4 groups of three.
Step-by-step explanation:
Given:
Total number of people attending the theater = 47
Total groups = 11 ( 3 or 5)
Number of groups of each size = ?
Let f be the number of groups of five
Let t be the number of groups of three
According to the question:
t + f = 11 -1
3t + 5f = 47 -2
Multiplying eq 1 with 3
3t + 3f = 33 -3
Solving equation 2 and 3:
3t + 5f = 47
3t + 3f = 33
____________________
2f = 14
f = 7
Substituting the value of f = 7 in equation 1 we get,
t + f = 11
t + 7 = 11
t = 4
Therefore, there are 7 groups of five and 4 groups of three.