if 28 a + 30 b + 31 c = 365 then find a + b + c ?

Concept

In any standard (non-leap) calendar year, the 365 days are spread across 12 months, and every month has either 28, 30, or 31 days. Exactly 1 month (February) has 28 days, exactly 4 months (April, June, September, November) have 30 days, and the remaining 7 months (January, March, May, July, August, October, December) have 31 days.

Working

1. Match the equation 28a + 30b + 31c = 365 to the real month-groups: a = number of 28-day months = 1, b = number of 30-day months = 4, c = number of 31-day months = 7.

2. Verify: 28×1 + 30×4 + 31×7 = 28 + 120 + 217 = 365, which matches the given total exactly.

3. Add the month counts: a + b + c = 1 + 4 + 7.

Cross-check

a, b, and c count three disjoint groups of months that together make up the entire year, so their sum must equal the total number of months in a year, confirming the result independently without recomputing from scratch.

So a + b + c = 12.