SOLUTION: Hello, I need help with the following problem: A mathematician works for {{{ t }}} hours per day and solves {{{ p }}} problems per hour, where {{{ t }}} and {{{ p }}} are pos

Question 1047022: Hello,
I need help with the following problem:
A mathematician works for hours per day and solves problems per hour, where and are positive integers and . One day, the mathematician drinks some coffee and discovers that he can now solve problems per hour. In fact, he only works for 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?
Thank you,
Nicole
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
(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 the day he drank coffee.
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