Charges $25 dollars for private tutoring and $18 for group tutoring. in one week a tutor earn $265 for 12 students. how many private and group sessions were there?

the number of private tutoring sessions is 7

the number of group tutoring session is 5

Step-by-step explanation:

Let x represent the number of private tutoring sessions.

Let y represent the number of group tutoring sessions.

In one week a tutor taught 12 students. This means that

x + y = 12

Charges $25 dollars for private tutoring and $18 for group tutoring. He earned $265 for that week. This means that

25x + 18y = 265 - - - - - - - - - - -1

Substituting x = 12 - y into equation 1, it becomes

25(12 - y) + 18y = 265

300 - 25y + 18 = 265

- 25y + 18 = 265 - 300

- 7y = - 35

y = - 35/ -7

y = 5

Substituting y = 5 into x = 12 - y, it becomes

x = 12 - 5

x = 7

  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).