Question

1

Sometimes scale drawings are shown on graph
paper. Each square on this graph paper is inch.
4
Use the scale drawing of the living room to answer
questions 4 and 5.
chair
chair
stereo
fireplace
sola
Scale-inch-18 inches
bookcase
door
television
There are 1,296 in.2 in one square yard. Use
a proportion to find out how many square
yards of carpet it would take to cover the
floor of the living room.
(1 point)
T
28 yd²
30 yd²
32 yd²
O 35 yd²

Answer 1

Approximately 324 square yards of carpet are needed to cover the living room floor. The correct answer is T, 28 yd², which is the closest option.

To determine the number of square yards of carpet needed to cover the floor of the living room, you can set up a proportion using the given scale of the drawing and the conversion factor for square inches to square yards.

The scale of the drawing is 1 inch = 18 inches. This means that 1 inch on the drawing corresponds to 18 inches in reality.

Now, since each square on the graph paper represents 1 square inch, the area of each square in reality is
`\(18 * 18 = 324\)` square inches.

The given conversion factor is that there are
`\(1,296\)` square inches in one square yard.

Let
`\(x\)` be the number of square yards of carpet needed. The proportion can be set up as follows:

`\[\frac{\text{Area on Drawing (square inches)}}{\text{Area in Reality (square inches)}} = \frac{\text{Number of Square Yards Needed}}{\text{Conversion Factor (square yards to square inches)}}\]`

`\[(324)/(1) = (x)/(1,296)\]`

Now, solve for \(x\):

`\[ x = (324 * 1,296)/(1) \]`

`\[ x = 420,768 \]`

So, the living room would require
`\(420,768\)` square inches of carpet. Now, convert this to square yards:

`\[ \text{Square Yards} = (420,768)/(1,296) \]`

`\[ \text{Square Yards} \approx 324 \]`

Therefore, it would take approximately
`\(324\)` square yards of carpet to cover the floor of the living room. The closest option is
`\(T\) (28 yd²).`