Question

Orchid wants to retile her bathroom floor, which has an area of 40 square feet. She is deciding between two types of custom tiles. The square tile is One-half foot by One-half foot and costs $0.45 per tile. The rectangular tile is 2 feet by One-fourth foot and costs $0.80 per tile.
Which tile should Orchid choose to minimize costs? Explain.

She should choose the square tiles because the total cost will be $8 less.
She should choose the rectangular tiles because the total cost will be $8 less.
She should choose the square tiles because the total cost will be $14 less.
She should choose the rectangular tiles because the total cost will be $14 less.

Answer 1

Your answer is the second option, she should choose the rectangular tiles because the total cost will be $8 less.

To find this answer we need to first find the total cost for using square tiles, and the cost for using rectangular tiles, and compare them. We can do this by finding the area of each tile individually, calculating how many tiles we would need, and multiplying this by the cost for one tile:

Square tiles:

The area of one square tile is 1/2 × 1/2 = 1/4 ft. Therefore we need 40 ÷ 1/4 = 160 tiles. If each tile costs $0.45, this means the total cost will be $0.45 × 160 = $72

Rectangular tiles:

The area of one rectangular tile is 2 × 1/4 = 2/4 = 1/2 ft. Thus we need 40 ÷ 1/2 = 80 tiles. Each tile costs $0.80, so the total cost will be 80 × $0.80 = $64.

This shows us that the rectangular tiles will be cheaper by $8.

I hope this helps! Let me know if you have any questions :)