There are 47 people attending a play at an outdoor theater. There are 11 groups of people sitting in groups of 3 or 5. How many groups of each size are there? This is about solving real-world problems with systems of linear equations -hint

There are 7 groups of five and 4 groups of three.

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.

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