Roberto was born on his grandmother's birthday. The two 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
Roberto shares his birthday with his grandmother. Their current ages
are reversed digits of one another, but the grandmother's age is a prime number.
Ten years from now, the grandmother's age is three times Roberto's age.
What are the current ages of Roberto and his grandmother?
Plans to Solve/Investigate the
A brief compilation of prime
numbers, from 2 to 100, is helpful in completing this problem. The prime
numbers (ages) then must be evaluated for reasonableness. The use of Excel
is helpful in completing this problem.
Investigation/Exploration of the
First, the set of prime numbers
from 2 to 100 were evaluated for reasonableness. The essential question is
if the grandmother's age (the prime number) were reversed, is it reasonable that
the resulting number could be Roberto's age? Since we are speaking of a
grandmother, ages should differ reasonably across a two generation span.
For the sake of example, if we
selected the prime number 53 as the grandmother's age, is it reasonable that
Roberto could be 35 years of age? 53 - 35 = 18. Is it reasonable
that Roberto and his grandmother's ages are 18 years apart? Not likely.
This process was continued until
there were four possible ages remaining of our set of prime numbers: 61,
71, 73 and 83.
I then completed a spreadsheet of
these possible ages to discover which combination met the other requirements of
Roberto's age (reverse of grandmother's age)
Roberto's age in 10 years
Grandmother's age in 10 years should be
3 times Roberto's age
If you examine Roberto's age in 10
years and the grandmother's age in 10 years, I am seeking a solution in which
the grandmother's age is is three times Roberto's age.
This relationship is found if the
grandmother's current age is 71and Roberto's current age is 17. In 10
years, grandma is 27 * 3 or 81.
We have a solution!
Extensions of the Problem
Does a solution exist where
grandmother's age is twice Roberto's age in ten years? Four times?
Author & Contact
Link(s) to resources, references, lesson plans, and/or other
to see problem listed on InterMath