Every math week, I plan to provide a math challenge which could take you seconds to hours to solve, assuming you don’t cheat by using technology to solve it for you.

Today, I offer a time filler I occasionally use while substituting a junior or senior high math class that has “completed” all of its work, usually before I even enter class. I learned this problem from Blaine Dowler of Sylvan Learning. Usually I reward the first person who solves it, and usually it is the “weakest” student who does it.

The challenge is: If the product of two numbers is two and their sum is five, what is the simplest sum of their inverses?

I would love to hear how you solved this challenge.

Good luck.

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x + y = 5

xy = 2

(x+y)/(xy) = 5/2

x/(xy) + y/(xy) = 5/2

1/y + 1/x = 5/2

Great work, JC. You found a/the quick way to solve this puzzle. Want to try your hand at my other challenges?