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Write-up


Title
Stamp Collecting
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?

 

Plans to Solve/Investigate the Problem

Because of the possible number of iterations, I decided to use Excel to set up and solve this problem. 

 

Investigation/Exploration of the Problem

I know that my second digit must be 3 times the last digit, and my first digit must be 1 (since the number is between 1000 and 2000.) In order for my second digit to be a unit number, my ones digit can not be bigger than 3 (4*3 = 12, which is not a unit number.)  Another constraint is that the ones digit must be odd, so this further limits my options to either 1 or 3. 

 

At this point, my first, second, and fourth digits are almost decided.  Look at the spreadsheet I created to show possible solutions.

a= 1 1 1
b= 3 9 9
c= 7 3                   0
d= 1 3 3
  Number of Stamps Number of Stamps Number of Stamps
1371 1933 1903
  sum of digits sum of digits sum of digits
12 16 13
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Extensions of the Problem

 

Author & Contact
Michelle Houston
mhouston@rockdale.k12.ga.us