Respuesta :
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 = [tex]\frac{1 inch}{4 feet}[/tex]
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
=[tex]\frac{1 inch}{4feet}=\frac{20 inch}{L}[/tex]
L = 80 feet
Real width of the office building on blueprint = B
[tex]\frac{1 inch}{4feet}=\frac{15 inch}{B}[/tex]
B = 60 feet
Area of the building = [tex]L\times B=80 ft\times 60=4800 ft^2[/tex]
Cost of project = $22,000
Cost of project per square foot =[tex]\frac{\$22,000}{4800 ft^2}=4.58 \$/ft^2[/tex]
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 = [tex]\frac{1 inch}{8 feet}[/tex]
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
=[tex]\frac{1 inch}{8feet}=\frac{10 inch}{L}[/tex]
L = 80 feet
Real width of the office building on blueprint = B
[tex]\frac{1 inch}{8feet}=\frac{8 inch}{B}[/tex]
B = 64 feet
Area of the building = [tex]L\times B=80 ft\times 64=5120 ft^2[/tex]
Cost of project = $25,000
Cost of project per square foot =[tex]\frac{\$25,000}{5120 ft^2}=4.88 \$/ft^2[/tex]
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 = [tex]\frac{1 inch}{6 feet}[/tex]
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
=[tex]\frac{1 inch}{6 feet}=\frac{15 inch}{L}[/tex]
L = 90 feet
Real width of the office building on blueprint = B
[tex]\frac{1 inch}{6feet}=\frac{12 inch}{B}[/tex]
B = 72 feet
Area of the building = [tex]L\times B=90 ft\times 72ft=6480 ft^2[/tex]
Cost of project = $27,000
Cost of project per square foot =[tex]\frac{\$27,000}{6480ft^2}=4.17\$/ft^2[/tex]
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 = [tex]\frac{1 inch}{12 feet}[/tex]
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
=[tex]\frac{1 inch}{12 feet}=\frac{8 inch}{L}[/tex]
L = 96 feet
Real width of the office building on blueprint = B
[tex]\frac{1 inch}{12feet}=\frac{6 inch}{B}[/tex]
B = 72 feet
Area of the building = [tex]L\times B=96 ft\times 72ft=6912 ft^2[/tex]
Cost of project = $27,000
Cost of project per square foot =[tex]\frac{\$30,000}{6912ft^2}=4.34\$/ft^2[/tex]
Project B > Project A > Project D > Project C
