Quandaries
and Queries 

The longestlived US presidents are John Adams(age90), Herbert Hoover (also90), and Harry Truman (88). Behind them are James Madison, Thomas Jefferson, and Richard Nixon. The lattter three men lived a total of 249 years, and their ages at the time of death form consecutive odd integers. For how long did Nixon, Jefferson, and Madison live? Please help me! My name is Lisa and I am a student in 10th grade. Your response would be deeply appreciated. Thank you. 

Hi Lisa, I think the best way to approach this problem is by intelligent, guess and check. Consecutive odd integers are odd integers that differ by 2, like 7,9,and 11 or 63,65 and 67. The presidents' ages at the time of death were three consecutive integers, so they were very close to the same age. If they were exactly the same age at the time of death and the sum of their ages was 249 then they each would have lived ^{249}/_{3} = 83 years. Can you complete the problem now? Penny 

