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Roberto and Granma!


Problem Statement
Roberto was born on his grandmother's birthday. The 2 digits of Roberto's age today are the reverse of the digits of his grandmother's age. The grandmother's age is a prime number. Ten years from now, his grandmother will be three times as old as Roberto will be then. How old are Roberto and his grandmother now?

Problem setup

After using the sieve of Eratosthenes, we found all of the prime numbers. After finding the prime numbers, we eliminated the ones that could not be the ages due to impossibility.


Plans to Solve/Investigate the Problem

We narrowed the choices down to 61, 71, 73 and 83 for the grandmother's age. The reversal of these numbers is Roberto's age. Then, we had to add ten years to the ages and triple Roberto's age and this must equal Granma's age.


Investigation/Exploration of the Problem

The only solution that will work is if Granma is 71 and Roberto is 17 now. This way, when you add 10 years to 17 and 71, you get 27 and 81. Then, when you triple 27, you get 81 which will be Granma's age ten years from now.

Pam Joseph