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A homeowner wants to replace the carpet in a room that is 11 feet 10 inches wide and 14 feet

9 inches long. She likes several different carpet styles and colors, with prices ranging from $19.95 to $22.95 per square yard. Removal of the old carpet and installation of a new pad and the new carpet will cost $6.89 per square yard. Assuming she decides not to use the most expensive of the carpet styles she likes, which is the best estimate of the cost to have new carpet installed?

1. $5600
2. $650
3. $580
4. $480

1 Answer

1 vote

Answer:

1. $560

Explanation:

Since the length and width are given in ft and in., first, we will conver the dimensions to inches. 1 ft = 12 in.

area of the room:

A = (11 ft 10 in.) × (14 ft 9 in.)

A = 142 in. × 177 in.

A = 25,134 in.²

1 yd = 36 in.

Now we convert the area into yd².

A = 25,134 in.² × (1 yd²)/(36 in.)²

A = 19.3935 yd²

The cheapest carpet costs $19.95/yd².

Add the cost of removal and installation of new pad: $19.95/yd² + $6.89/yd² = $26.84/yd².

The most expensive carpet costs $22.95/yd².

Add the cost of removal and installation of new pad: $22.95/yd² + $6.89/yd² = $29.84/yd².

The range of prices per square yard is from $26.84/yd² to 29.85/yd².

The cheapest carpet will cost:

19.3935 yd² × 26.84/yd² = $520.52

The most expensive carpet will cost:

19.3935 yd² × 29.84/yd² = $578.70

The price is between $520.52 and $578.70.

Choices 2. $650 and 4. $480 are eliminated.

She is not using the most expensive carpet, so it will cost less than $578.70, so choice 3. $580 is eliminated.

Answer: 1. $560

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