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?

107 days...

Maybe this is a weird way to think about it, but let’s say you have A days that rained in the afternoon, M days that rained in the morning, and C days that were completely clear all day.

A+M = 100
A+M+C = what we wanted to find as the answer to the problem.

The number of mornings that were clear equals the number of rainy afternoons (because then the morning is clear) plus the number of totally clear days.
A+C = 95

Similarly, the number of afternoons that were clear equals the number of rainy mornings (because then the afternoon is clear) plus the number of totally clear days.
M+C = 19.

A = 95-C
M = 19-C

A+M = (95-C) + (19-C) = 100
114 – 2C = 100
14 = 2C
C = 7

So A+M+C = 100+7 = 107

So there were 107 days altogether

Posted by nikki on 2004-11-02 13:15:31