+367 A mathematician works for \(t\) hours per day and solves \(p\) problems per hour, where \(t\) and \(p\) are positive integers and \(1 . One day, the mathematician drinks some coffee and discovers that he can now solve \(3p+7\) problems per hour. In fact, he only works for \(t-4 \) hours that day, but he still solves twice as many problems as he would in a normal day. How many problems does he solve the day he drinks coffee?
+54 He solves 112 problems the day he drinks coffee
(3p+7)(t-4) = 2tp
===> .
Since both t and p are positive integers, can only take on the values 0, 1, or 2. (Why?)
does not yield any value of p.
===> p = 7.
===> p = 0, which is not acceptable.
Therefore, p = 7,
===> ,
and the mathematician solved (3*7 + 7)(8-4) = 28*4 = 112 problems
