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?

In my old grammar school days I think we did these like this...

If we designate Morning/Rain as Mr, Afternoon/Clear as Ac etc. etc. then we know:

Mr + Ar = 100 (total days when it rained)

Mc = 95 (given)

Ac = 19 (given)

there are a fixed number of days all of which have a morning and an afternoon (Duh!)

Mr + Mc = Ac + Ar

therefore

Mr + 95 = 19 + Ar

subtracting 95 from both siudes

Mr = Ar - 76

Adding Ar to both sides

Mr + Ar = Ar - 76 + Ar

substituting our equation for Mr + Ar, and collecting terms

100 = 2Ar - 76

2Ar = 176

Ar = 88

if it was clear on 19 afternoons and raining on 88 then there were 107 days

Posted by Pete on 2004-11-02 13:28:50