It costs a family $305.00 to buy a 16-ft-by-18-ft rug. If the cost is proportional to the area, what will it cost the family to buy a 8-ft-by-9-ft rug?
a. $145.42
b. $570.39
c. $76.25
d. $288.00
The area of the 16-ft-by-18-ft rug is 16 x 18 = 288 square feet.
To find the cost per square foot, we can divide the total cost by the area:
305 ÷ 288 = 1.06
This means that the cost per square foot is $1.06.
The area of the 8-ft-by-9-ft rug is 8 x 9 = 72 square feet.
To find the cost of this rug, we can multiply the area by the cost per square foot:
72 x 1.06 = $76.32
Therefore, the family will need to pay $76.32 to buy the 8-ft-by-9-ft rug.
The closest answer choice is (c) $76.25, which is a reasonable approximation given that we rounded the cost per square foot to two decimal places.
To find out the cost of a smaller rug, we need to determine the ratio of the areas of the two rugs.
The first rug has dimensions 16 ft by 18 ft, so its area is: 16 ft × 18 ft = 288 square feet.
The second rug has dimensions 8 ft by 9 ft, so its area is: 8 ft × 9 ft = 72 square feet.
To find the ratio, we divide the area of the first rug by the area of the second rug: 288 square feet ÷ 72 square feet = 4.
Since the cost of the rug is proportional to the area, we can multiply the cost of the first rug by the ratio to find the cost of the second rug: $305.00 × 4 = $1220.00.
However, none of the answer choices provided is $1220.00. Therefore, none of the given answer choices is correct.