If the broker received a 6.5 percent commission that was $10,400, what was the sales price of the house?

If the broker received a 6.5 percent commission that was $10,400, what was the sales price of the house?

• A. 160,000
• B. 155,000
• C. 150,000
• D. 165,000

Answer: (A)

When a commission is a percentage of the sale price, you can find the price by dividing the commission earned by the rate. Here, the commission is 6.5% (0.065) and the earned amount is 10,400. So the sale price = 10,400 ÷ 0.065 = 160,000. Check: 0.065 × 160,000 = 10,400, which matches. Quick comparisons show that 150,000 gives 9,750 and 165,000 gives 10,725, so 160,000 is the exact amount that yields the 10,400 commission.

When a commission is a percentage of the sale price, you can find the price by dividing the commission earned by the rate. Here, the commission is 6.5% (0.065) and the earned amount is 10,400. So the sale price = 10,400 ÷ 0.065 = 160,000. Check: 0.065 × 160,000 = 10,400, which matches. Quick comparisons show that 150,000 gives 9,750 and 165,000 gives 10,725, so 160,000 is the exact amount that yields the 10,400 commission.