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A mathematician works for t hours per day and solves p problems per hour, where t and p are positive integers and 1 (By the way, I in no way are trying to cheat. I just want to know a way to solve this, as all the solutions i got were invalid)

 Jan 31, 2023
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By Simon's Favorite Factoring Trick, the equation reduces to (p + 7)(t - 12) = 11.

 

The factors of 11 are 1 and 11.  Since p + 7 must be at least 7, p + 7 = 11 and t - 12 = 1.  Then p = 4 and t = 13.

 

Therefore, when the mathematician drinks coffee, he solves 2pt = 2*4*13 = 104 problems.

 Jan 31, 2023

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