Discussion
The average age of 40 students is 16 years. If the teacher's age is also included, the average becomes 17 years. What is the age of the teacher ?
Answer: D
The teacher is 57 years old.
Compare the total ages before and after the teacher is included:
\[ \begin{aligned} \text{Students} &= 40 \times 16 = 640 \\ \text{With teacher} &= 41 \times 17 = 697 \\ \text{Teacher} &= 697 - 640 = 57 \end{aligned} \]
Shortcut: the teacher must supply his own share of the new average (17) plus one extra year for each of the 40 students, which is 17 + 40 = 57.
A teacher of 56 would make the new total 696, an average just under 17, and 48 or 60 miss it by more. Only 57 makes the average of all 41 people exactly 17.
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