# The ship's model To assemble my model of a sailboat I need some raft wood slats. In the modeling shop they sell them in boxes of a dozen and also in loose units although they are somewhat more expensive. So I ordered several boxes and some loose units to complete exactly what I needed.

As I had no money on me, the clerk, who is my friend, pointed it in my account, handed me the bag with the order and I left.

When I got home, I discovered that the clerk was wrong and that he had given me as many boxes as single units I had asked for and as many single units as boxes I had asked so that I have exactly half the slats I needed.

How many slats do I need to assemble the model?

#### Solution

If we call X to the number of boxes e Y to the amount of loose units
Y T to the total slats I need we have to:

If I equal both equations to eliminate T we have to

Where do we get that:

This equation has infinite integer solutions but since the number of single units will be less than 12 (since if I wouldn't ask for a complete box) the only possible solution is X = 23 and Y = 10. I ordered 23 boxes and 10 units that are 286 slats and yet they gave me 10 boxes and 23 slats that are 143 slats, exactly half of what I need.