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.

the last choice

step-by-step explanation:

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).