Question

Mr. and Mrs. Harper are planning to install a deck and a garden. Help them determine which of the two choices below is most efficient. Plan A: Deck measures 18 feet by 25 feet, garden measures 9 feet by 12 feet. Plan B: Deck measures 16 feet by 20 feet, garden measures a radius of 5 feet. If it costs $4.20 per square foot to install the deck, what is the cost for Plan A and Plan B?

a. Plan A: $10,710; Plan B: $6,300
b. Plan A: $7,560; Plan B: $5,280
c. Plan A: $9,450; Plan B: $5,280
d. Plan A: $10,710; Plan B: $5,280

Answer 1

Plan A costs $2,343.60 and Plan B costs $1,672.70.

Step-by-step explanation:

To determine the cost for each plan, we need to calculate the area of the deck and the garden for each option.

Plan A:

Deck area = Length x Width = 18 ft x 25 ft = 450 sq ft

Garden area = Length x Width = 9 ft x 12 ft = 108 sq ft

Total area for Plan A = Deck area + Garden area = 450 sq ft + 108 sq ft = 558 sq ft

Cost for Plan A = Total area x Cost per square foot = 558 sq ft x $4.20 = $2,343.60

Plan B:

Deck area = Length x Width = 16 ft x 20 ft = 320 sq ft

Garden area = (pi x Radius^2) = (3.14 x 5 ft^2) = 78.5 sq ft

Total area for Plan B = Deck area + Garden area = 320 sq ft + 78.5 sq ft = 398.5 sq ft

Cost for Plan B = Total area x Cost per square foot = 398.5 sq ft x $4.20 = $1,672.70

Therefore, the cost for Plan A is $2,343.60 and the cost for Plan B is $1,672.70.