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Printjmc
prealgebra intermediate
Problem
What is the sum of all the positive two-digit integers where one of the digits is three times the other?
Solution
We have two cases:
Case 1: The tens digit is three times the unit digit. In this case we have and
Case 2: The unit digit is three times the tens digit. In this case we have and
Sum up the two cases: we have
Case 1: The tens digit is three times the unit digit. In this case we have and
Case 2: The unit digit is three times the tens digit. In this case we have and
Sum up the two cases: we have
Final answer
264