During a certain period of days in Cucumberland recently it was observed that when it rained in the afternoon, it had been clear in the morning, and when it rained in the morning, it was clear in the afternoon. (In a given morning or afternoon, it is either raining or it is clear.) It rained on 100 days, and was clear on 19 afternoons and 95 mornings. How many days were there altogether?

There are only 3 types of days:

A = rain morning, clear afternoon

B = clear morning, rain afternoon

C = clear all day  (It is clear from the problem that it can't rain all day)

The info in the problem yields a system of 3 equations

(1) A+B=100; (2) B+C=95; (3) A+C=19

What we want is A+B+C so we only need one of the variables.

Subtracting (2) from (1) yields (4) A - C = 5

Adding (4) and (3) yields 2A = 24 so A=12

This and (2) gives the solution: A + B + C = 12 + 95 = 107

-Jer

Posted by Jer on 2004-11-02 17:11:29