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
square inches.
The given conversion factor is that there are
square inches in one square yard.
Let
be the number of square yards of carpet needed. The proportion can be set up as follows:
![\[\frac{\text{Area on Drawing (square inches)}}{\text{Area in Reality (square inches)}} = \frac{\text{Number of Square Yards Needed}}{\text{Conversion Factor (square yards to square inches)}}\]](https://img.qammunity.org/2024/formulas/mathematics/college/9td71lxwipukz3vgxnj889ikfjexjhxxtd.png)
![\[(324)/(1) = (x)/(1,296)\]](https://img.qammunity.org/2024/formulas/mathematics/college/ujq4178wf8btnlkg0w4agbppbwbor6biqf.png)
Now, solve for \(x\):
![\[ x = (324 * 1,296)/(1) \]](https://img.qammunity.org/2024/formulas/mathematics/college/xbsxswd7mf0fq1169xfti0h0p92rbdcc08.png)
![\[ x = 420,768 \]](https://img.qammunity.org/2024/formulas/mathematics/college/41bjuvl2kjhs431dja78op3dnjtbhhbtzm.png)
So, the living room would require
square inches of carpet. Now, convert this to square yards:
![\[ \text{Square Yards} = (420,768)/(1,296) \]](https://img.qammunity.org/2024/formulas/mathematics/college/we2kxm1tvn8y4o2dneldr2fx5chq2pcihs.png)
![\[ \text{Square Yards} \approx 324 \]](https://img.qammunity.org/2024/formulas/mathematics/college/905whml97pjbkq3u6d32mpa93guw472y1c.png)
Therefore, it would take approximately
square yards of carpet to cover the floor of the living room. The closest option is
