Question 1047022
(3p+7)(t-4) = 2tp

===> {{{t = 4*((3p+7)/(p+7)) = 4*(3 - 14/(p+7))}}}.

Since both t and p are positive integers, {{{14/(p+7)}}} can only take on the values 0, 1, or 2.  (Why?)

{{{14/(p+7) = 0}}} does not yield any value of p.
{{{14/(p+7) = 1}}} ===> p = 7.
{{{14/(p+7) = 2}}} ===> p = 0, which is not acceptable.

Therefore, p = 7, 

===> {{{t = 4*((3*7+7)/(7+7)) = 8}}},

and the mathematician solved (3*7 + 7)(8-4) = 28*4 = 112 problems the day he drank coffee.