+845 A mathematician works for t hours per day and solves p problems per hour, where and are positive integers. One day, the mathematician drinks some coffee and discovers that he can now solve 4p+5 problems per hour. In fact, he only works for t-3 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?
+130071 The number of problems he solves on a normal day = p*t
On the day he drinks coffee he solves 2pt problems....so...
(4p + 5) ( t - 3) = 2pt
4pt +5t - 12p - 15 = 2pt
2pt + 5t - 12p - 15 = 0
2pt + 5t = 12p + 15
t = [ 12p + 15 ] / [ 2p + 5 ]
Note that this makes t an integer when p= 5 and t = 5
So.....he solves 2(5)(5) = 50 problems on the day he drinks coffee
