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A box contains many candies.
If 3 candies are taken away, the rest can be shared evenly among 7 people.
If 5 are taken away, the rest can be shared evenly among 8 people.
If  3 candies are added, then the box can be shared evenly among  5 people.
What is the smallest number of candies in the box?

 Apr 2, 2021
 #1
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N - 3   =  7a    ⇒   N  =   7a  + 3

N - 5  =   8b   ⇒    N  =   8b  + 5

N + 3  =  5c    ⇒   N  =   5c  -  3

 

7a  + 3   =  5c  - 3

5c - 7a   =   6    ⇒   c = ( 7a + 6)  /  5

 

5c - 3  =  8b + 5

5c - 8b  =  8   ⇒   c  =  ( 8b+ 8)  /  5

 

 

7a  +  6  =  8b + 8

 

7a  - 8b     =   2

 

a      b              N

6      5          not  possible                           

14   12        not possible                                 

22   19            157

 

 

Smallest  number of  candies in the  box = 157

 

 

cool cool cool

 Apr 2, 2021

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