Need to find out how many paper clips Brian has.

Question

Brian has some boxes of paper clips.  Some boxes hold 10 clips and some boxes hold 100.  He has some paper clips left over.  He has three more boxes with 100 paper clips than he has boxes with 10 paper clips.  He has two fewer paper clips left over than he has number of boxes with 100 paper clips.  Whap number of paper clips could he have?

Answer 1

Let's assume that Brian must have fewer than 10 paperclips left over (otherwise he would have put them in a box of 10). Since there are only a few possible values for the number of paperclips Brian might have left over (any number from 1 to 9), we can just list them out.


If Brian has 1 paperclip left over, then he has 3 100s boxes (since there are two fewer leftovers than 100s boxes), but 0 10s boxes (since there are three more 100s boxes than 10s boxes). The problem told us he had some 10s boxes, so this scenario doesn't work.

If Brian has 2 paperclips left over, then he has 4 100s boxes (since there are two fewer leftovers than 100s boxes) and 1 10s box (since there are three more 100s boxes than 10s boxes).

If Brian has 3 paperclips left over, then he has 5 100s boxes and 2 10s boxes.

If Brian has 4 paperclips left over, then he has 6 100s boxes and 3 10s boxes.

If Brian has 5 paperclips left over, then he has 7 100s boxes and 4 10s boxes.

If Brian has 6 paperclips left over, then he has 8 100s boxes and 5 10s boxes.

If Brian has 7 paperclips left over, then he has 9 100s boxes and 6 10s boxes.

If Brian has 8 paperclips left over, then he has 10 100s boxes and 7 10s boxes.

If Brian has 9 paperclips left over, then he has 11 100s boxes and 8 10s boxes.


Each of these scenarios gives you a possible number of paperclips Brian might have. For example, with 2 leftovers, 4 100s boxes, and 1 10s box, Brian has a total of:

(4×100) + (1×10) + (2×1) = 400 + 10 + 2 = 412 paperclips