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?
Figure out how many stamps Jessica
has based on the clues given. The answer must be between 1000-2000 and
must be an odd number. The sum of the digits must = 12. The hundreds
digit = 3 times the ones digit.
Plans to Solve/Investigate the
The thousands digit must be 1.
Use guess and check to determine the other digits.
Investigation/Exploration of the
The ones digit must be 1, 3, 5, 7, or
9 in order for the number to be an odd number. It can't be 9, 7, 5, or 3
since the hundreds digit would have to be 27, 21, 15, or 9. 27, 21, & 15
are impossible since they are not single digits. If the ones digit was 3,
the hundreds digit would be 9. Then the digits 1 (thousands place), 9
(hundreds place), and 3 (ones place) would equal more than 12. So the ones
digit must be 1. That would mean the hundreds place would be 3. 1
(thousands place), 3 (hundreds place), and 1(ones place) equal 5 so the tens
digit must be 7. That would mean the number of stamps is 1371. This
is an odd number between 1000 and 2000. The sum of its digits equals 12.
The hundreds digit, 3, is three times the ones digit, 1.
1 + 3 + 7 + 1 = 12. 3 x 1 = 3
Jessica has 1,371 stamps.
Extensions of the Problem
Investigate to discover the closest
solution that would not use any digits more than once. One possible
solution to this might be 1,953. This odd number is still between 1,000
and 2,000, and the hundreds digit is still three times the ones digit. The
exception is that the digits equal 18.
Look to see if there is any
correlation between the number of stamps being an odd number yet the sum of its
digits is an even number. The above solution is still an example of an odd
number with its sums equaling an even number. If the solution was 1,632,
the digits equal 12 - an even number with its sum equaling an even number.
But the hundreds digit is still 3 times the ones digit. What other
solutions along this line could you find?
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