Question

Describe the steps you would use to solve this problem. In a scale drawing of a dining room floor plan, 10mm equals 2 meters. If the homeowners wanted to purchase flooring that costs $10.89 per square yard, how much would they spend on flooring for the dinning room? The demensions of the dining room on the floor plan are 40 mm x 32 mm.

Answer 1

To solve the problem, first determine the actual dimensions of the dining room using the scale factor of 1/200, then calculate the area in square meters, next convert to square yards, and finally compute the total cost of flooring based on the cost per square yard.

Step-by-step explanation:

To solve the problem, we need to calculate the actual dimensions of the dining room in meters, determine the area in square meters, and then convert that area into square yards to calculate the total cost of flooring.

Calculate the dimensions using the scale factor: 10 mm equals 2 meters implies a scale factor of 1/200. So, the actual dimensions of the floor are 40 mm x 1/200 = 0.2 meters and 32 mm x 1/200 = 0.16 meters.

Compute the area in square meters: 0.2 meters x 0.16 meters = 0.032 square meters.

Convert square meters to square yards (1 square meter = 1.19599 square yards): 0.032 square meters x 1.19599 = 0.0383 square yards.

Multiply area by cost per square yard to find the total cost: 0.0383 square yards x $10.89 = $0.417. However, since we cannot buy a fraction of a yard of flooring, the homeowner will need to purchase at least 1 square yard. Therefore, the cost would be $10.89 for the dining room floor.

Answer 2

666.95 $

Step-by-step explanation:

If In a scale drawing of a dining room floor plan 10 mm = 2 meters

then 40 mm = (40 × 2) / 10 = 8 meters

and 32 mm = (32 × 2) / 10 = 6.4 meters

area of the dining room = 8 × 6.4 = 51.2 m²

1 square yard = 0.836 squared meters (m²) and it costs 10.89 $

Now we devise the following reasoning:

if 0.836 m² of flooring costs 10.89 $

then 51.2 m² of flooring costs X $

X = (51.2 × 10.89) / 0.836 = 666.95 $