Number Theory

 

You have a total supply of $1000$ pieces of candy, and an empty vat.  You also have a machine that can add exactly $5$ pieces of candy per scoop to the vat, and another machine that can remove exactly $3$ pieces of candy with a different scoop from the vat.  When these two machines are done, there is only one piece of candy left in the vat.  What is the smallest possible number of times the the first machine added candy to the vat?    

 

Let the 1^st machine cycle 2 times          2 x 5  =  10  pieces added       

Let the 2^nd machine cycle 3 times           3 x 3  =   9  pieces removed    

                                                                               1  piece remaining     

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