Math Question, help appreciated.

How many wheels does a bicycle have?
How many on a trike?
There are 20 frames and some are bikes and some are trikes.
There are 48 wheels and 3 are on each trike and 2 on each bike.

Put these two facts together and the number of bikes and trikes will become obvious.

Rap

1. B = Number of bicycles, T = number of tricycles
There are 48 wheels.

B + T = 20

2B + 3T = 48
2B + 3(20 - B) = 48
2B + 60 - 3B = 48
60 - B = 48
B = 12

Therefore, since B + T = 20, T = 8.

Verify: 2 (12) + 3 (8) = 24 + 24 = 48.

Bricks:

There are three dimensions (4, 5, and 9) that can be used as the height of a brick.

Since there are four bricks, the heights must be combined in one of the following four ways:

1) 4 of the same height
2) 3 at one height, one at a different height
3) 2 at one height, 2 at another height
4) 2 at one height, 1 aha different height, and 1 at a third height

There are 3 ways for number 1,
6 ways for number 2,
3 ways for number 3, and
3 ways for number 4.

It turns out that all of the combinations result in uinque heights, so duplicates don't need to be eliminated.

Grand total = 15