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Math Counts Message Board › Math Challenge

Math Challenge

Martin C.
Trenton, NJ
Post #: 2
Marilyn vos Savant writes a weekly Ask Marilyn column in the Parade newspaper insert, which comes with the Sunday Inquirer. Two weeks ago she gave an incorrect answer to a math question. See http://parade.condena...­ I sent an email to the column and was told that there will be a correction in the column for July 13. The particular problem was not very interesting and can be easily solved using high school math. If a and b are the project times for Angelina and Brad, they satisfy 6/a + 6/b = 1.

A more interesting problem is to show that Marilyn's assumption that a+b=24 is incorrect. Can you give an argument without using algebra to show that if a < b then a + b > 24?

Can you give a purely algebraic proof?
Given 0 < a < b and
6/a + 6/b =1
Show a + b > 24.
It can be done using nothing more than middle school math using insights from the non-algebraic proof.
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