Question

An architecture firm creates blueprints for office buildings. Last week, they produced four rectangular blueprints for four different projects. Project A: A 20-inch by 15-inch blueprint with a scale of 1 inch to 4 feet and a projected cost of $22,000. Project B: A 10-inch by 8-inch blueprint with a scale of 1 inch to 8 feet and a projected cost of $25,000. Project C: A 15-inch by 12-inch blueprint with a scale of 1 inch to 6 feet and a projected cost of $27,000. Project D: An 8-inch by 6-inch blueprint with a scale of 1 inch to 12 feet and a projected cost of $30,000. Order the projects from greatest to least projected cost per square foot of the actual offices. Project C Project B Project D Project A

Answer 1

Cost in decreasing order: Project B>Project A>Project D>Project C

Explanation:

Project A

Area:
`A=20 in*15 in= 300 in^2`

Scale:
`S=(4 ft *4ft)/(1 in*1in)=16 (ft^2)/(in^2)`

Cost:

`C=(22000)/(300 in^2*16 (ft^2)/(in^2))`

`C=(4.58)/(ft^2)`

Project B

Area:
`A=10 in*8 in= 80 in^2`

Scale:
`S=(8 ft *8ft)/(1 in*1in)=64 (ft^2)/(in^2)`

Cost:

`C=(25000)/(80 in^2*64 (ft^2)/(in^2))`

`C=(4.88)/(ft^2)`

Project C

Area:
`A=15 in*12 in= 180 in^2`

Scale:
`S=(6 ft *6ft)/(1 in*1in)=36 (ft^2)/(in^2)`

Cost:

`C=(27000)/(180 in^2*36 (ft^2)/(in^2))`

`C=(4.16)/(ft^2)`

Project D

Area:
`A=8 in*6 in=48 in^2`

Scale:
`S=(12 ft *12ft)/(1 in*1in)=144 (ft^2)/(in^2)`

Cost:

`C=(30000)/(48 in^2*144 (ft^2)/(in^2))`

`C=(4.34)/(ft^2)`