Remark
My problem is not telling you what the answer should be. The answer is C. My problem is telling you why A B and D are wrong.
What the question is saying is that every lesson costs 9 dollars We don't know how many lessons there were. Call it x. There is a one time charge of 45 dollars and x lessons have been taken. The average cost is 12 dollars.
12 = (45 + 9x) / x which is C
A: is wrong. All that happened is that A has added 9 + 45 which is 54. That's to be divided by the number of lessons taken. That's not what the problem says.
B: is wrong because every time a lesson is taken 9 is divided by the number of lessons. The second term (9/x) keeps on getting smaller and smaller. The equation for B is somehow saying that every time you take a lesson you are paying 45 dollars + 9/the number of lessons. So for the 10th lesson you would pay 45 + 9/10 dollars = 45.90 Your total to the 10th lesson is saying that you are paying 450 dollars + the sum of 9 + 4.5 + ... 0.90 That's not the intent.
D: is wrong (but sneaky wrong) That's the description for 1 lesson. 9 does require an x in the numerator. I almost picked D.