Question 27

The cost per square foot of Marlene's rug is $6.

To calculate the cost per square foot of Marlene's circular rug, we first find the area of the rug using the formula for the area of a circle, A = πr². For a radius of 3 feet, the area is approximately 28.27 square feet. Dividing the total cost of $169 by the area gives a cost of about $6 per square foot.

A) 6

This option is correct as the calculated cost per square foot is indeed $6. By determining the area of the rug as approximately 28.27 square feet and dividing the total cost of $169 by this area, the result confirms that the cost per square foot is $6.

B) 12

This option is incorrect because it suggests a cost per square foot that is double the calculated value. If the cost were $12 per square foot, the total cost would need to be $339.24, which does not match the actual cost of $169.

C) 18

This option is also incorrect as it implies an even higher cost per square foot. A cost of $18 per square foot would result in a total cost of approximately $509.86, which is significantly more than the actual cost of the rug.

D) 24

This option is incorrect because it indicates an excessively high cost per square foot. If the cost were $24 per square foot, the total cost would be around $678.48, far exceeding the actual price of the rug.

Conclusion

The correct answer is definitively $6 per square foot, as all calculations based on the rug's dimensions and total cost confirm this value. The other options fail because they suggest cost per square foot figures that would lead to total costs exceeding the given price of the rug, thereby demonstrating a misunderstanding of the area and pricing relationship.