A vacant land parcel was sold for $200 per front foot. If the broker earns a 10% commission and the salesperson has a 60% share of that commission, how much does she receive?

A vacant land parcel was sold for $200 per front foot. If the broker earns a 10% commission and the salesperson has a 60% share of that commission, how much does she receive?

• A. $960
• B. $1,200
• C. $1,600
• D. $1,280

Answer: (A)

The amount the salesperson earns comes from the commission on the sale price, broken down by the given split. The sale price depends on the frontage: price per front foot times the number of front feet. The broker’s commission is 10% of that sale price, and the salesperson receives 60% of the broker’s commission. So the salesperson’s payoff equals 0.60 × 0.10 × (front feet × 200) = 12 × (front feet). If there are 80 front feet, that’s 12 × 80 = 960. Equivalently, with 80 front feet the sale price is 80 × 200 = 16,000; the broker earns 10% of that, 1,600, and the salesperson receives 60% of 1,600, which is 960.

The amount the salesperson earns comes from the commission on the sale price, broken down by the given split. The sale price depends on the frontage: price per front foot times the number of front feet. The broker’s commission is 10% of that sale price, and the salesperson receives 60% of the broker’s commission.

So the salesperson’s payoff equals 0.60 × 0.10 × (front feet × 200) = 12 × (front feet). If there are 80 front feet, that’s 12 × 80 = 960. Equivalently, with 80 front feet the sale price is 80 × 200 = 16,000; the broker earns 10% of that, 1,600, and the salesperson receives 60% of 1,600, which is 960.