Intermath | Workshop Support
 Write-up

Title
Collecting Stamps problem

Problem Statement
Jessica has an odd number of stamps in her collection. The sum of the digits in the number of stamps she has is 12. The hundreds digit is three times the ones digit. If she has between 1000 and 2000 stamps in her collection, how many stamps does Jessica have?

Problem setup

Jessica has between 1,000 and 2,000 stamps in her collection. The number of stamps she has is an odd value.  If you add up the digits in the numbers of stamps she has, the sum will be 12.  The hundreds digit in the number of stamps she has is three times as large as the ones digit.  From this can we find how many stamps Jessica has in her collection?

Plans to Solve/Investigate the Problem

With the information presented in the problem, I can logically solve the problem step-by-step.  There will be a bit of guess-and-check involved also.

Investigation/Exploration of the Problem

There are four place values that need to be filled in:  ___   ___  ___  ___.   The ones place has to be occupies by an odd digit (1, 3, 5, 7, or 9).  The only possible choices for the ones digit are 1 and 3; any larger value will not allow three times the value to be placed in the hundreds place.

If 3 is is the ones place, then 9 is in the hundreds place making a total of 12 without putting any digits in the tens or thousands places at all.  This cannot be correct.  Thus the ones digit has to be 1, making 3 the hundreds digit.

There are two more place values to fill in.  The sum of these other two digits has to be 8 in order to add to the 1 and 3  (sum = 4) for a four-digit total of 12.  The number of stamps is between 1,000 and 2,000; this means that the thousands digit has to be 1.  Anything greater would give a value greater than 2,000.  The missing digit in the tens place is 7.

The final number of Jessica's collected stamps is 1,371.

Extensions of the Problem

>The number of stamps could be an even number.

>The number of stamps could be between 10,000 and 20,000.

>The sum of the digits could be 15, 20, etc.

Author & Contact
Rita J. Rogers
rrogers@rockdale.k12.ga.us