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A school orders $99$ textbooks, all for the same price. When the bill for the total order comes, the first and last digits are obscured. What are the missing digits?
_18,486.7_

 Jul 17, 2024

Best Answer 

 #3
avatar+1249 
+2

 

A school orders $99$ textbooks, all for the same price.    

When the bill for the total order comes, the first and last    

digits are obscured. What are the missing digits?    
_18,486.7_    

 

What is the criterion for a correct answer?  If we can get       

a price per book that comes out even?  What about that      

the price of a book is a plausible amount?  You decide.       

 

                                               518,486.76     

                                              ––––––––––  =  5,237.24     

                                                      99              

 

 

.

 Jul 18, 2024
 #2
avatar+280 
0

THIS is not possible

https://web2.0calc.com/questions/number-theory_66931

 Jul 18, 2024
edited by BRAINBOLT  Jul 18, 2024
 #3
avatar+1249 
+2
Best Answer

 

A school orders $99$ textbooks, all for the same price.    

When the bill for the total order comes, the first and last    

digits are obscured. What are the missing digits?    
_18,486.7_    

 

What is the criterion for a correct answer?  If we can get       

a price per book that comes out even?  What about that      

the price of a book is a plausible amount?  You decide.       

 

                                               518,486.76     

                                              ––––––––––  =  5,237.24     

                                                      99              

 

 

.

Bosco Jul 18, 2024
 #4
avatar+1249 
+1

 

Disclosure:  Maxematics gave me the idea how to find the answer       

when s/he pointed out that the product would be a multiple of nine,     

and therefore the digits in the product have to add up to a multiple     

of nine.  After that, I used brute force.    

.    

Bosco  Jul 18, 2024
 #5
avatar+118678 
+2

Rather than using brute force Bosco you could have used this division fact

 

Divisibility rule of 11: This particular rule states that the given number can only be completely divided by 11 if the difference of the sum of digits at odd position and sum of digits at even position in a number is 0 or 11.

 Sep 3, 2024

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