Question

Mathematical modeling is a process whereby a real world problem or situation is described in mathematical language. Research and share a real world problem, situation, phenomenon, or event that can be modeled using a linear equation or inequality. Post the mathematical model describing your application if available.

Answer 1

Illustration of a real world problem or situation : Let us consider we have a room of 6 m in length and 5 m in breadth. We need to cover the floor of this room with square mosaic tiles of side 30 cm. What is the number of tiles that we will require? We will understand this by building a mathematical model.

Arrangement : Formulation : We need to consider the room's area and the tile's area for tackling the problem. The side of the tile is 0.3 m. Since the length is 6 m, we can fit in tiles along the length of the room in one column.

Since the room is 5 meters in breadth, we have . Along these lines, we can fit in 16 tiles in a column. Since 16 × 0.3 = 4.8, 5 – 4.8 = 0.2 meters along the breadth will not be secured by tiles. This part should be secured by cutting alternate tiles. The broadness of the floor left uncovered, 0.2 meters, is the greater part the length of a tile, which is 0.3 m. So we can't break a tile into two equivalent parts and utilize both the parts to cover the rest of the part.

Mathematical Description : We have:

Total number of tiles required = (Number of tiles along the length

× Number of tiles along the breadth) + Number of tiles along the area uncovered ----------(1)

Arrangement : As we said over, the quantity of tiles along the length is 20 and the number of tiles along the breadth is 16. We require 20 more tiles for the last row. Substituting these values in (1), we get (20 × 16) + 20 = 320 + 20 = 340.

Understanding : We require 340 tiles to cover the floor.

Approval : In actuality, an artisan may request that we get some additional tiles to

supplant those that get harmed while slicing them to measure. This number will obviously

rely on the ability of your artisan! In any case, we require not alter Equation (1) for this.

This gives us a rough thought of the quantity of tiles required. In this way, we can stop here.