+1501 A mathematician works for t hours per day and solves p problems per hour, where t and p are positive integers. One day, the mathematician drinks some coffee and discovers that he can now solve 3p + 12 problems per hour. In fact, he only works for t - 7 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?
+1950 We can write an equation to solve this problem. We have
(3p+12)(t−7)=2tp
Now, factoring the left side, we get
3pt−21p+12t−84=2tp12t+pt−21p=84pt=21p−12t+84pt=7(3p+12)−12tpt+12t=7(3p+12)t(p+12)=7(3p+12)t/7=3p+12p+12
We could test some values here, since no time was given. t has to be less than 24 and a multiple of 7.
When t is 7, p is 0.
When t is 14, p is 12.
When t is 21, p is undefined.
Thanks! :)
