Discussion
The average age of 2 teachers and 6 students is 14 years. All the 6 students are of same age and the 2 teachers are also of same age. The difference between the age of a teacher and a student is 24 years, then what is the age of a teacher?
Answer: C
A teacher is 32 years old.
Let a student be s years old and a teacher \(s + 24\). The total age of the 8 people is \(8 \times 14 = 112\).
\[ \begin{aligned} 2(s + 24) + 6s &= 112 \\ 8s + 48 &= 112 \Rightarrow s = 8 \\ \text{teacher} &= 8 + 24 = 32 \end{aligned} \]
Check: \(2 \times 32 + 6 \times 8 = 64 + 48 = 112\). Each of the other options fails this check: a teacher of 34, for example, makes a student 10 and the total 128.
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