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Algebra Level 3

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?

The answer is 107.

1 solution

Danish Ahmed
Jan 22, 2015

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 $A+B+C$

Adding the equations , we get $2(A + B + C) = 214$

So $A + B + C = \boxed{107}$ which is the required answer.

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The answer is 107.

1 solution

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