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Title
Collecting Stamps Problem Discussion

Problem Statement
With the given set of information, how many stamps exist in Jessica's stamp collection?

Problem setup

This problem is similar to the Missing Number problem that was completed in class.

 

Jessica has between 1,000 and 2,000 stamps in her collection.  I have been provided with the following facts:  there is an odd number of stamps in the collection, the hundreds digit is three times the ones digit, and the sum of the digits of the number of stamps is 12.

 

Plans to Solve/Investigate the Problem

My initial strategy is to exclude certain digits from the ones place, since there must an odd number of stamps in the collection.  Secondly, I must consider possibilities for the hundreds and ones digits, given that the hundreds digit must be three times the ones digit.

 

I will try differing combinations of numbers, primarily using the guess and check strategy for possible solutions that fulfill the predetermined requirements.

 

Investigation/Exploration of the Problem

Initially, I tried nine as the hundreds digit and three as the ones digit.  Since the sum of the number of stamps must be twelve, this option fails since twelve is achieved without the other two digits.  Next, six and three were considered as possibilities for the hundreds and ones digits.  This fulfills the requirement that there be an odd number of stamps and the requirement that the hundreds digit be three times the ones digit.  Other possibilities for the hundreds and ones digit were eliminated because they were not multiples of three.

 

 

                 6                      3         (the sum of these digits is 9)

 

A sum of nine has been achieved.  There are between 1,000 and 2,000 stamps in the collection.  If the thousands place was assigned a value of 2, or 2,000, the number of stamps in the collection would exceed the limit of 2,000, as prescribed in the problem.

 

     1            6           2            3       

 

 I will check this solution against the requirements of the problem.  There is an odd number of stamps.  The sum of the digits is 12.  The hundred digit, 6, is three times the ones digit, 3.  There are between 1,000 and 2,000 stamps in the collection.  1,623 is the solution to the problem.

 

Extensions of the Problem

How would the possible answer change if an even number of stamps existed in the stamp collection?

 

How would possible solutions change if there were between 3,000 and 4,000 stamps in the stamp collection?

 

How would your solution change if the sum of the digits were 14? 15? 16?

Author & Contact
Angela Gilliam, Memorial Middle School, Conyers, GA
agilliam@rockdale.k12.ga.us

Link(s) to resources, references, lesson plans, and/or other materials
Click here to view the problem on the InterMath site

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