Problema Solution
A local toy store sells whistles in packages of 3, 6, or 12. If you need 30 whistles for a party, in how many different combinations can you buy them?
There a ____ different ways to buy 30 whistles
Answer provided by our tutors
This is one of those problems that is difficult to explain the method. It's more of a brute force thing.
Start with the smallest package exclusively 3 to a pack.
3 goes in thirty ten times so our first combination is
10 packs of 3
From there, we can exchange two packs of three with a pack of six and four packs of six with a pack of 12. This gives us combinations like
8 packs of 3, 1 pack of 6
6 packs of 3, 2 packs of 6
6 packs of 3, 1 pack of 12
4 packs of 3, 3 packs of 6
4 packs of 3, 1 pack of 6, 1 pack of 12
2 packs of 3, 4 packs of 6
2 packs of 3, 2 packs of 6, 1 pack of 12
2 packs of 3, 2 packs of 12
From there, we are out of combinations with 3, so we start again with 6. 6 goes into 30 5 times, so...
5 packs of 6
3 packs of 6, 1 pack of 12
1 pack of 6, 2 packs of 12
And 12 alone cannot add up to thirty so these are all of our possible combinations.
If you count them, you'll observe...
There are 12 different wats to buy 30 whistles.