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Help with algebra

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A mathematician works for t hours per day and solves p problems per hour, where t and p are positive integers and 1 < p < 20. One day, the mathematician drinks some coffee and discovers that he can now solve 3p + 1 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?

Jul 11, 2021

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$(3p+1)(t-4)=2tp$

$3tp - 12p + t - 4 = 2tp$

$tp - 12p + t - 4 = 0$

$t(p+1) = 12p + 4$

$t(p+1) = 4(3p + 1)$

$t = 4 \left(\frac{3p+1}{p+1}\right)$

$t = 4 \left(\frac{3p + 3 - 2}{p+1}\right)$

$t = 4 \left(3 - \frac{2}{p+1}\right)$

$t \leq 24$

Continue with https://web2.0calc.com/questions/the-powers-of-coffee-in-mathematicians#r2

Jul 11, 2021