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 A Project C Project B

Answer 1

The order from greatest to least :

Project B > Project A > Project D > Project C

Explanation:

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.

Scale factor =
`(1 inch)/(4 feet)`

Length of the office building on blueprint = l =20 inch

Width of the office building on blueprint = b =15 inch

Real length of the office building on blueprint = L

=
`(1 inch)/(4feet)=(20 inch)/(L)`

L = 80 feet

Real width of the office building on blueprint = B

`(1 inch)/(4feet)=(15 inch)/(B)`

B = 60 feet

Area of the building =
`L* B=80 ft* 60=4800 ft^2`

Cost of project = $22,000

Cost of project per square foot =
`(\$22,000)/(4800 ft^2)=4.58 \$/ft^2`

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.

Scale factor =
`(1 inch)/(8 feet)`

Length of the office building on blueprint = l =10 inch

Width of the office building on blueprint = b =8 inch

Real length of the office building on blueprint = L

=
`(1 inch)/(8feet)=(10 inch)/(L)`

L = 80 feet

Real width of the office building on blueprint = B

`(1 inch)/(8feet)=(8 inch)/(B)`

B = 64 feet

Area of the building =
`L* B=80 ft* 64=5120 ft^2`

Cost of project = $25,000

Cost of project per square foot =
`(\$25,000)/(5120 ft^2)=4.88 \$/ft^2`

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.

Scale factor =
`(1 inch)/(6 feet)`

Length of the office building on blueprint = l =15 inch

Width of the office building on blueprint = b =12 inch

Real length of the office building on blueprint = L

=
`(1 inch)/(6 feet)=(15 inch)/(L)`

L = 90 feet

Real width of the office building on blueprint = B

`(1 inch)/(6feet)=(12 inch)/(B)`

B = 72 feet

Area of the building =
`L* B=90 ft* 72ft=6480 ft^2`

Cost of project = $27,000

Cost of project per square foot =
`(\$27,000)/(6480ft^2)=4.17\$/ft^2`

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

Scale factor =
`(1 inch)/(12 feet)`

Length of the office building on blueprint = l = 8 inch

Width of the office building on blueprint = b =6 inch

Real length of the office building on blueprint = L

=
`(1 inch)/(12 feet)=(8 inch)/(L)`

L = 96 feet

Real width of the office building on blueprint = B

`(1 inch)/(12feet)=(6 inch)/(B)`

B = 72 feet

Area of the building =
`L* B=96 ft* 72ft=6912 ft^2`

Cost of project = $27,000

Cost of project per square foot =
`(\$30,000)/(6912ft^2)=4.34\$/ft^2`

Project B > Project A > Project D > Project C