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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. One day, the mathematician drinks some coffee and discovers that he can now solve $4p+7$ 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?

 Aug 23, 2023
 #1
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The number of problems he solves on  a  normal  day  =  p*t

 

On the day he drinks coffee  he solves 2pt problems....so...

 

(4p + 7) ( t - 3)  = 2pt

 

4pt +7t - 12p - 21  = 2pt

 

2pt +  7t - 12p - 21 =  0

 

2pt + 7t = 12p + 21

 

t =  [  12p + 21 ]  / [ 2p + 7 ] 

 

Note that  this makes t an nteger when   p= 7  and t =  5

 

So.....he solves    2(7)(5) =    70 problems on the  day  he  drinks  coffee

 

cool cool cool

 Aug 24, 2023
edited by CPhill  Aug 30, 2023

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