Question

If the screws are sold in boxes offiftyunits and nuts in boxesFour. FiveHow many boxes of each do we have to buytohave a thread for each screw?

Answer 1

The total number of screws is a multiple of

fifty

and that of nuts is a multiple of

Four. Five

. We must calculate the lcm.

We decompose the numbers:

fifty = two ⋅ 5 two Four. Five = 3 two ⋅ 5

For the lcm we use all the bases to the greatest exponent. Therefore,

m c m ( Four. Five , fifty ) = two ⋅ 3 two ⋅ 5 two = 450

To have

450

screws, we need

9  boxes, and to have

450 nuts, 10  boxes.

In total, we must buy

19  boxes.

Answer 2

If no box remains empty, then we can have (1,1,3) or (1,2,2) distribution pattern.

When boxes are kept in a row, they will treated as different. In this case the number of ways will be 5−1C3−1=4C2=6.