Number of problems normally answered per day is
p * t
So......when he drinks coffee, he solves
(3p + 7) (t - 4) problems....and this is twice the number he normally answers...so...
(3p + 7) (t - 4) = 2p*t
3pt + 7t - 12p - 28 = 2pt
pt + 7t - 12p - 28 = 0
We have an equation with two unknowns....so....there will possibly be more than one solution
WolframAlpha shows that the (possible) feasible solutions are
p = 1 t = 5 = 5 problems on a regular day
p = 7 t = 8 = 56 problems on a normal day
So as a check
(3*1 + 7)(5 - 4) = (2)(1*5) ??
(10)(1) = 10 is true
(3*7 + 7) (8 - 4) = (2)(7*8) ???
(28) (4) = 112
112 = 112 is also true
So.......the number of problems that he answers when he drinks coffee is either
(3)(1) + 7 = 10 problems per day
or
(3)(7) + 7 = 112 problems per day