Question 1093502: Gerry,his older brother Tommy, and their father are prime number ages. If you multiply them together it equals 3055. If you add them together it equals 65. What are their ages from youngest to oldest?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
If the ages are all prime numbers and their product is 6055, then one of the ages must be 5. So Gerry is 5 years old.
The other two ages multiply to 3055/5 = 611 and add to 65-5=60. You could solve that algebraically using
 and
However, the algebraic solution would probably end up requiring some trial and error, so it is almost certainly easier to get to the final answer by logical trial and error.
We need two ages that are appropriate for a father and son, are prime numbers, and have a sum of 60. Look for such pairs of numbers and find one for which the product is 611.
Note that you have another clue to help narrow down the search. If the product of two numbers ends in the digit 1 and the sum ends in the digit 0, then the last digits of the two number have to be 3 and 7. Since the two ages need to be appropriate for the older brother of a 5-year-old and the father of the two boys, the only likely candidates are 13 and 47, or 17 and 43.
And one of those pairs gives you the correct product of 611, giving you the answer to the problem.
Answer by ikleyn(52788)  (Show Source):
You can put this solution on YOUR website! .
The decomposition of the number 3055 into the product of prime numbers is unique:
3055 = 5*13*47.
So, the answer is: the youngest is 5 years old, his brother is 13 years old, and the father's age is 47 years.
The info about the sum of their ages is UNNECESSARY, EXCESSIVE and IS NOT USED in the solution.
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