Question 1168057: Hi
For every book bob sells he will make 12 dollars. He will. Get another 5 dollars for every set of 10 books he sells. If he sells 100 books he will get a 50 dollar bonus . How many books did he sell to make 1372 dollars.
Thanks
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
First of all, it is clear that Bob's earning is monotonic 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 ANSWER: 106 books should be sold.
The solution is completed.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
His income from selling the books is not linear; but it is always increasing. So, as the other tutor suggests, the easiest way to solve the problem is just to make a reasonable guess and work from there.
He gets $1200 for selling 100 books, not counting the bonuses. Since that is a bit less than the total he makes including bonuses, let's find his total income, including bonuses, for selling 100 books.
$12 * 100 = $1200 ($12 for each book)
$5 * 10 = $50 ($5 bonus for each group of 10 books)
$50 *1 = $50 ($50 bonus for selling 100 books)
Total: $1300
Since he made $1372, we know the number of books he sold was more than 100. So our guess of 100 books was a good starting place.
The difference between the $1372 he made and the $1300 he makes for selling 100 books is $72.
That is what he makes for selling $72/$12 = 6 books; and he won't get any additional bonuses for selling 6 more books after the first 100.
So the number of books he sold is 106.
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