Answer: the number of private tutoring sessions is 7
the number of group tutoring session is 5
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