How Many Days in the Month?

Date: 01/22/2004 at 15:09:18
From: Nicole
Subject: Adding fractions and whole numbers

There were 11 days of rain one month in Boston.  Of the remaining
days, two-fifths were sunny, one-fourth were cloudy, and it snowed the
other 7 days.  How many days were in the month?  I don't know whether
I need to change the whole numbers to fractions or change the
fractions to decimals in order to find out how many days were in the
month.

Date: 01/22/2004 at 15:34:25
From: Doctor Terrel
Subject: Re: Adding fractions and whole numbers

Hi Nicole,

Thanks for writing.  This is kind of a tricky problem, but there is
one key idea that I think will help you solve it.  Notice that the
first two sentences split the month into two distinct parts; one part
has 11 days of rain and the other part has 'the remaining days.'  The
7 days of snow are included in the 'remaining days' and are not a
separate part.

So let's put the 11 days part aside for now and focus on the
'remaining days' part.  We don't know how many days are in there, but
the problem says that it's possible to take one-fourth of that number
and also two-fifths of that number.  Since we can't have fractions of
days, both of those calculations must come out evenly.  That's the key!

We know that the total number of days in a month has to be 31 or less.
Can you find a number less than 31 that you would be able to take
one-fourth of and two-fifths of and get clean results?  If so, that
should be the number of days in the 'remaining days' part of the month.

Be sure to make all the calculations and check to see if your answer
makes sense.

Does that help?  Write back if you are still confused and tell me what
you've tried.

- Doctor Terrel, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 01/23/2004 at 08:30:46
From: Nicole
Subject: Thank you (Adding fractions and whole numbers)

Thank you so much Dr. Math.  You really broke the problem down for me,
and before I finished reading your answer, it all made sense!