Average of a and b is 42. Average of b and c is 56. Average of c and a is 48.…

Concept

Concept: The average of n quantities equals their total sum divided by n. For three numbers a, b and c, average = (a + b + c) / 3. A useful identity: the average of the three pairwise averages of a, b and c equals the average of a, b and c itself, because each variable appears the same number of times across the pairs.

Application

1. Each pairwise average gives a pair-sum: a + b = 2 x 42 = 84.

2. b + c = 2 x 56 = 112.

3. c + a = 2 x 48 = 96.

4. Add all three pair-sums: (a + b) + (b + c) + (c + a) = 84 + 112 + 96 = 292. The left side counts each variable twice, so it equals 2(a + b + c). Hence 2(a + b + c) = 292, giving a + b + c = 146.

5. Average of a, b and c = (a + b + c) / 3 = 146 / 3 = 48.666... This decimal does not terminate; among the given options it is represented as 48.66.

Cross-check

Cross-check: averaging the three given pairwise averages directly, (42 + 56 + 48) / 3 = 146 / 3, gives the same non-terminating value 48.666..., matching the result above.