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Chapter 10: Problem 40

A rectangular room measures 12 feet by 15 feet. The entire room is to be covered with rectangular tiles that measure 3 inches by 2 inches. If the tiles are sold at ten for \(\$ 1.20\), what will it cost to tile the room?

Short Answer

Expert verified
The cost to tile the room is \$518.40.

Step by step solution

01

Convert All Measurements to a Consistent Unit

Firstly, convert the measurement of the tiles from inches to feet. Given that 1 foot = 12 inches. Thus, each tile measures \( \frac{1}{4} \) feet by \( \frac{1}{6} \) feet.
02

Calculate the Area of the Room and the Tile

The room's area can be calculated by multiplying its length and breadth, which is 12 feet x 15 feet = 180 square feet. The area of each tile is \( \frac{1}{4} \) feet x \( \frac{1}{6} \) feet = \( \frac{1}{24} \) square feet.
03

Find the Number of Tiles

To find the number of tiles required to cover the room, divide the room鈥檚 area by the area of a tile. This is 180 square feet / \( \frac{1}{24} \) square feet per tile = 4320 tiles.
04

Determine the Number of Packs of Tiles

Since tiles are sold in packs of ten, divide the total number of tiles by 10 to find out how many packs of tiles are needed. This is 4320 tiles / 10 tiles per pack = 432 packs.
05

Calculate the Total Cost

Finally, multiply the number of packs by the price per pack to find the total cost. This is 432 packs x \$1.20 per pack = \$518.40.

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