A rectangular lot is 150 ft by 200 ft and sells at an expressly applicable $8.50 per square foot of total area. What total sale price follows?
Correct Answer
C) $255,000
Area=150 ft×200 ft=30000 SF; price=30000 SF×8.50 dollars/SF=255000 dollars. Common errors: converting to square yards before applying the per-square-foot rate gives $28,333; misplacing the decimal in the area gives $25,500; misplacing the decimal in the rate gives $2,550,000.
Why This Is the Correct Answer
Option C is correct because the lot area is 150 ft x 200 ft = 30,000 SF, and 30,000 SF x $8.50 per SF = $255,000. The rate is stated per square foot of total area, so no unit conversion is needed. Price per square foot is one of the standard units of comparison for land.
Why the Other Options Are Wrong
Option A: $25,500
Option A, $25,500, results from misplacing the decimal in the area: 150 x 200 x $8.50 / 10 = $25,500, as if the lot were 3,000 SF. The correct area is 30,000 SF, giving 30,000 x $8.50 = $255,000.
Option B: $28,333
Option B, $28,333, results from converting to square yards before applying a per-square-foot rate: 150 x 200 x $8.50 / 9 = $28,333. The rate is per square foot, so the correct price is 30,000 SF x $8.50 = $255,000.
Option D: $2,550,000
Option D, $2,550,000, results from misplacing the decimal in the rate: 150 x 200 x $8.50 x 10 = $2,550,000, as if the rate were $85 per SF. The correct price is 30,000 SF x $8.50 = $255,000.
Match units, then multiply
Get the area in the same unit as the rate, then multiply area by rate.
How to use: Use this on any land price calculation that gives a per-unit rate.
Exam Tip
Check that your area unit matches the rate unit, and do a quick estimate (30,000 x about $8 is about $240,000) to catch decimal errors.
Common Mistakes to Avoid
- -Converting square feet to square yards when the rate is per square foot
- -Misplacing the decimal in the area or the rate
- -Using perimeter instead of area
Concept Deep Dive
Analysis
This question tests a simple area-times-unit-price calculation. Find the area in square feet, then multiply by the price per square foot. Area is 150 ft x 200 ft = 30,000 SF, and 30,000 SF x $8.50 = $255,000.
Background Knowledge
Land is often compared using units such as price per front foot, per square foot, per acre, per building site or per buildable unit. The unit chosen should match how the market prices similar land. Keeping units consistent, such as square feet with a per-square-foot rate, avoids conversion errors.
Real-World Application
An appraiser analyzing vacant commercial lots finds that recent sales cluster around a consistent price per square foot. Applying that rate to the subject's measured area gives a value indication. The appraiser double-checks the area units to avoid square-yard or decimal mistakes.
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