Question 1168057
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First of all, it is clear that Bob's earning is <U>monotonic</U> function of the number of books sold.


Let consider some values.


If the number of books is 100, then he gets


    12*100              = 1200 dollars counting $12 for each single  book, PLUS

     5*(100/10)   = 5*10 =  50 dollars counting   $5 for every  10 sold books, PLUS

     50*(100/100) = 50*1 =  50 dollars counting  $50 for every 100 sold books, 

     which gives the TOTAL  1200 + 50 + 50 = 1300 dollars.



If the number of books is 101, then he gets


    12*101                  = 1212 dollars counting $12 for each single  book, PLUS

     5*int(101/10)   = 5*10 =  50 dollars counting   $5 for every  10 sold books, PLUS

     50*int(101/100) = 50*1 =  50 dollars counting  $50 for every 100 sold books, 

     which gives the TOTAL  1212 + 50 + 50 = 1312 dollars.



If the number of books is 102, then he gets


    12*102                  = 1224 dollars counting $12 for each single  book, PLUS

     5*int(102/10)   = 5*10 =  50 dollars counting   $5 for every  10 sold books, PLUS

     50*int(100/100) = 50*1 =  50 dollars counting  $50 for every 100 sold books, 

     which gives the TOTAL  1224 + 50 + 50 = 1324 dollars.


In this solution, the expression  int(x)  denotes the function "whole part of the number x".


So, if x is the number of the sold books, then Bob's earning is

    Earning(x) = 12*x + 5*int(x/10) + 50*int(x/100).


With this formula, we can calculate further for n = 103, 104, 105, 106


     Earning(103) = 12*103 + 5*int(103/10) + 50*int(103/100) = 12*103 + 5*10 + 50*1 = 1336,

     Earning(104) = 12*104 + 5*int(104/10) + 50*int(104/100) = 12*104 + 5*10 + 50*1 = 1348,

     Earning(105) = 12*105 + 5*int(105/10) + 50*int(105/100) = 12*105 + 5*10 + 50*1 = 1360,

     Earning(106) = 12*106 + 5*int(106/10) + 50*int(106/100) = 12*106 + 5*10 + 50*1 = 1372.


In this way, we get the <U>ANSWER</U>: 106 books should be sold.
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The solution is completed.