11. taylor purchased 30 square feet of carpet to cover the floor area in her closet that measures 5 1/4 feet…
11. taylor purchased 30 square feet of carpet to cover the floor area in her closet that measures 5 1/4 feet by 4 2/3 feet. how many square feet of carpet will be left over after taylor carpets her closet floor?\n\na. 6 1/2 square feet\nb. 7 square feet\nc. 24 square feet\nd. 5 1/2 square feet
Answer
Answer:
D. 5 1/2 square feet
Explanation:
Step1: Convert mixed - numbers to improper fractions
$5\frac{1}{4}=\frac{5\times4 + 1}{4}=\frac{21}{4}$; $4\frac{2}{3}=\frac{4\times3+2}{3}=\frac{14}{3}$
Step2: Calculate the area of the closet floor
Area = length×width, so $A=\frac{21}{4}\times\frac{14}{3}=\frac{21\times14}{4\times3}=\frac{294}{12} = 24.5$ square feet
Step3: Calculate the remaining carpet area
Remaining area = purchased area - used area. Purchased area is 30 square feet. So $30 - 24.5=5.5 = 5\frac{1}{2}$ square feet