Collecting Stamps

Problem: 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?

Solution: We must find the digits in the number of stamps. Because the number is between 1000 and 2000, we know that the number but contain four digits. Let's represent this number by denoting the unknown digits as:

A B C D

First, we know that the number we are looking for must be an odd number. Therefore we know that D must be either 1, 3, 5, 7, or 9.

Second, The problem also states that the sum of the digits in the number is 12.

A + B + C + D = 12

Third, the hundreds digit is three times the ones digit.

B = 3D

A must be a 1 because this is the only way that the four digit number can be between 1000 and 2000.

1 B C D

Since B = 3D and D must be either 1, 3, 5, 7, or 9, we can deduce that D could only be 1 or 3 because then B would still be able to be a one digit number.

1 3D C D

Now let's try some combinations:

1 9 C 3

This could not work because 1 + 9 + 3 = 13 which is already higher than the given sum of 12.

1 3 C 1

1 + 3 + C + 1 = 12

C = 7

We have found our number! 1371. Jessica has 1371 stamps in her collection. Thats A LOT of stamps!!

Reference: Project INTERMATH

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