1. tile problem

The question is:

Find the number of square tiles required to fill a given rectangle. If you use only part of a tile, then the rest is placed in the trash and can't be used.

Here is how I modeled it:

$\displaystyle n = \lceil{\frac{x}{t}}\rceil \times \lceil{\frac{y}{t}}\rceil$

Where n is the number of tiles required, x is the width of the rectangle, y is the length of the rectangle, and t is the size of the square tile.

Given some actual data:

The rectangle measures 25ft x 20ft.
The tile measures 2ft x 2ft.

$\displaystyle \lceil{\frac{25}{2}}\rceil \times \lceil{\frac{20}{2}}\rceil = 130$ tiles.

I'm running on like 2 hours of sleep, so I guess I'm just looking for verification that I'm doing this right. Thanks!

2. Basically, you just divide the total area of the rectangle, by the area of the squares tiles, and that is how many you will need.

So, 500 divided by 4= 125

You did the problem right, its just that 25/2 times 20/2 is equal to 125, not 130.

you must have done your math wrong.

3. I don't think I did the math wrong, but please correct me if I'm wrong:

$\displaystyle \lceil{\frac{25}{2}}\rceil \times \lceil{\frac{20}{2}}\rceil$

$\displaystyle \lceil{12.5}\rceil \times \lceil{10}\rceil$

$\displaystyle 13 \times 10$

$\displaystyle 130$

But, I think your equation differs from mine in that mine ceils the numbers before multiplying them. I'm doing that to obey the constraint "If you use only part of a tile, then the rest is placed in the trash and can't be used."