Consistent current dwelling cost new is $318,750 for 2,550 sf. What cost per square foot results?
Correct Answer
B) $125.00
318750÷2550 = 125. Common errors: misplacing the decimal (dividing by 25,500) gives $12.50; rounding the area to 2,500 sf before dividing gives $127.50; misplacing the decimal (dividing by 255) gives $1,250.00.
Why This Is the Correct Answer
Option B is correct because $318,750 ÷ 2,550 sf = $125.00 per square foot. This unit rate is the square foot cost that, applied back to 2,550 sf, reproduces the $318,750 total. No rounding of the area is needed or appropriate.
Why the Other Options Are Wrong
Option A: $12.50
Option A, $12.50, comes from misplacing the decimal by dividing by 25,500 instead of 2,550: $318,750 ÷ 25,500 = $12.50. The correct division is $318,750 ÷ 2,550 = $125.00.
Option C: $127.50
Option C, $127.50, comes from rounding the area to 2,500 sf before dividing: $318,750 ÷ 2,500 = $127.50. Using the actual 2,550 sf gives $125.00.
Option D: $1,250.00
Option D, $1,250.00, comes from misplacing the decimal by dividing by 255: $318,750 ÷ 255 = $1,250.00. The correct calculation is $318,750 ÷ 2,550 = $125.00.
Dollars over feet
Cost per square foot is dollars on top, square feet on the bottom. Check the result by multiplying it back by the area.
How to use: Use the multiply-back check to catch decimal errors on unit cost questions.
Exam Tip
Estimate first: $318,750 is a bit more than $300,000, and 2,550 is a bit more than 2,500, so the answer should be near $120 to $130.
Common Mistakes to Avoid
- -Misplacing the decimal when dividing by the area
- -Rounding the area before dividing
- -Dividing area by cost instead of cost by area
Concept Deep Dive
Analysis
This question tests the basic square foot cost calculation. Cost per square foot is total cost divided by the area, so $318,750 is divided by 2,550 sf. The wrong choices come from decimal placement errors or rounding the area before dividing.
Background Knowledge
The square foot method combines construction costs into one unit of measure, price per square foot, which is applied to the subject's area. Deriving a unit cost from a total cost and area is the reverse of that application. Consistent measurement of the area is essential for a reliable rate.
Real-World Application
A builder's contract shows a total dwelling cost of $318,750 for a 2,550 sf house. The appraiser converts it to a per-square-foot rate to compare with cost service figures and other recent builds in the market.
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