A parcel of land is 10 acres. How many 50 foot by 100 foot lots could be subdivided from the property if 26,000 square feet were dedicated for roads?

A parcel of land is 10 acres. How many 50 foot by 100 foot lots could be subdivided from the property if 26,000 square feet were dedicated for roads?

• A. 82
• B. 81
• C. 83
• D. 80

Answer: (B)

Think in terms of area and how many full lots fit in the usable space. Convert everything to square feet, subtract the road area, then divide by the size of one lot and take only whole lots. Ten acres is 10 × 43,560 = 435,600 square feet. Subtract the road dedication: 435,600 − 26,000 = 409,600 square feet available for lots. Each lot is 50 × 100 = 5,000 square feet. So how many 5,000-square-foot lots fit into 409,600? 409,600 ÷ 5,000 = 81.92, which means only 81 full lots can be laid out. A fraction of a lot isn’t possible, so 82 lots would require 82 × 5,000 = 410,000 square feet, more than what’s available by 400 square feet. Hence the maximum is 81 full lots.

Think in terms of area and how many full lots fit in the usable space. Convert everything to square feet, subtract the road area, then divide by the size of one lot and take only whole lots.

Ten acres is 10 × 43,560 = 435,600 square feet. Subtract the road dedication: 435,600 − 26,000 = 409,600 square feet available for lots. Each lot is 50 × 100 = 5,000 square feet. So how many 5,000-square-foot lots fit into 409,600? 409,600 ÷ 5,000 = 81.92, which means only 81 full lots can be laid out. A fraction of a lot isn’t possible, so 82 lots would require 82 × 5,000 = 410,000 square feet, more than what’s available by 400 square feet. Hence the maximum is 81 full lots.