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The average age of a class of 59 students and their teacher is 22 years and 4 months. If the average age of the class falls by four months when the teacher is excluded, what is the age (in years) of the teacher?

Question

The average age of a class of 59 students and their teacher is 22 years and 4 months. If the average age of the class falls by four months when the teacher is excluded, what is the age (in years) of the teacher?

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Solution

Sure, let's solve this step by step:

  1. The total age of the class including the teacher is 22 years and 4 months times 60 (59 students + 1 teacher). Convert 4 months into years by dividing by 12, so 4/12 = 0.33 years. Therefore, the total age is 22.33 years * 60 = 1339.8 years.

  2. The total age of the class excluding the teacher is 22 years times 59 (since the average age fell by four months, or 0.33 years, when the teacher was excluded). Therefore, the total age is 22 * 59 = 1298 years.

  3. The age of the teacher is the difference between the total age including the teacher and the total age excluding the teacher. So, the teacher's age is 1339.8 years - 1298 years = 41.8 years.

So, the teacher is approximately 42 years old (rounding up 41.8 years).

This problem has been solved

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