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```
Date: 09/20/2000 at 22:55:06
From: Melissa Bailey

During a recent span of time, 11 days had some rain. A morning rain
was always followed by a clear afternoon, and an afternoon rain was
preceded by a clear morning. In all, nine mornings and 12 afternoons
were clear. How many days had no rain at all?

I have no idea where to start.
```

```
Date: 09/21/2000 at 12:47:27
From: Doctor Rick

Hi, Melissa.

Start by thinking through what you know, and what you don't know.

We have some unknown total number of days. It rained on 11 of those
days. It didn't rain on the others, and this latter number is what you

You know that it never rains both morning and afternoon of the same
day. If it rains in the morning, it won't rain in the afternoon. If it
rains in the afternoon, it didn't rain that morning.

You know that there were 9 mornings without rain, and 12 afternoons
without rain.

How do we put this information together? Here's a question: how many
different kinds of day could there be?

-- No rain
-- Rain in morning              \ rain sometime
-- Rain in afternoon            /
--------------------------------
Total number of days

Pick one of these and define it as a variable. Then see if you can
write expressions for the others using that variable. I'll start. You
might define

x = days without rain

since that's what we want to find. Then you can start filling in the
table:

-- No rain               x
-- Rain in morning       ?     \ rain sometime   11
-- Rain in afternoon     ?     /
--------------------------------
Total number of days    11+x

Why is the total number of days equal to 11+x? Because it rained on 11
days, and the total is the sum of the days without rain and the days
with rain.

See what you can do to finish the table. Then you can write an
equation in x, and solve it to answer the question.

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra
Middle School Word Problems

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