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sukhopar [10]
2 years ago
13

An architecture firm creates blueprints for office buildings. Last week, they produced four rectangular blueprints for four diff

erent 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
Mathematics
1 answer:
Readme [11.4K]2 years ago
4 0

Answer:

The order from greatest to least :

Project B > Project  A > Project  D > Project  C

Step-by-step 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 = \frac{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

=\frac{1 inch}{4feet}=\frac{20 inch}{L}

L = 80 feet

Real width of the office building on blueprint = B

\frac{1 inch}{4feet}=\frac{15 inch}{B}

B = 60 feet

Area of the building = L\times B=80 ft\times 60=4800 ft^2

Cost of project = $22,000

Cost of project per square foot =\frac{\$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 = \frac{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

=\frac{1 inch}{8feet}=\frac{10 inch}{L}

L = 80 feet

Real width of the office building on blueprint = B

\frac{1 inch}{8feet}=\frac{8 inch}{B}

B = 64 feet

Area of the building = L\times B=80 ft\times 64=5120 ft^2

Cost of project = $25,000

Cost of project per square foot =\frac{\$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 = \frac{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

=\frac{1 inch}{6 feet}=\frac{15 inch}{L}

L = 90 feet

Real width of the office building on blueprint = B

\frac{1 inch}{6feet}=\frac{12 inch}{B}

B = 72 feet

Area of the building = L\times B=90 ft\times 72ft=6480 ft^2

Cost of project = $27,000

Cost of project per square foot =\frac{\$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 = \frac{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

=\frac{1 inch}{12 feet}=\frac{8 inch}{L}

L = 96 feet

Real width of the office building on blueprint = B

\frac{1 inch}{12feet}=\frac{6 inch}{B}

B = 72 feet

Area of the building = L\times B=96 ft\times 72ft=6912 ft^2

Cost of project = $27,000

Cost of project per square foot =\frac{\$30,000}{6912ft^2}=4.34\$/ft^2

Project B > Project  A > Project  D > Project  C

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