Paper clip totals

Question

Brian has some boxes of paper clips. Some hold 10, some hold 100. He has some clips left over. He has 3 more boxes with 100 than boxes with 10. He has 2 fewer clips left than number of boxes with 100. What number of clips could he have?

Answer 1

  X is the number of 10-count boxes

 

 

  The number of 100-count boxes is X+3

 

 The stray clips are X+3-2 = X+1

 

 Now you can generate the number of paper clips by selecting a positive value for X.

 

 Suppose he has x=1 box containing 10 paper clips.

Then he has 4 boxes containing 100 clips each and 2 stray paper clips.

Therefore he has 10 + 4*100 + 2 = 412

 

The general formula for the total number of paper clips is

 

 10x + 100(X+3) + (X+1) =

 10x + 100x + 300 + x + 1 = 

 111x + 301

 

Notice than when x=1, 111(1) + 301 = 412