Answer:
$52
Explanation:
Given 7 lessons are $82 and 11 lessons are $122, you want the cost of 4 lessons.
Equation
We assume the cost of lessons is a linear function, so its slope will be the same everywhere. This means we can write an equation reflecting this fact:
change in cost / change in lessons = (122 -82)/(11 -7) = (x -82)/(4 -7)
where x is the cost of 4 lessons.
Solution
-3(40/4) = x -82 . . . . . . multiply by -3, simplify
52 = x . . . . . . . . . . . . add 82
The cost of 4 lessons is $52.
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Additional comment
Adding 4 lessons adds $40 to the cost, so the cost of each is $10, in addition to a $12 fixed fee. (12+10·4 = 52)