A property owner wants to net at least $47,300 after paying a 5% broker's commission and paying $1,150 in closing costs. At what price must it sell?

A property owner wants to net at least $47,300 after paying a 5% broker's commission and paying $1,150 in closing costs. At what price must it sell?

• A. 51,000
• B. 50,500
• C. 52,000
• D. 49,000

Answer: (A)

Think of the net proceeds as the selling price minus the broker’s commission (5% of the price) and minus the closing costs. If the selling price is P, the net is P minus 0.05P minus 1,150, which is 0.95P minus 1,150. Set this equal to the target net of 47,300: 0.95P − 1,150 = 47,300 0.95P = 48,450 P = 48,450 ÷ 0.95 = 51,000 So the property must sell for 51,000 to net 47,300. Checking: 5% of 51,000 is 2,550; subtracting 2,550 and 1,150 from 51,000 leaves 47,300. Lower prices would yield a smaller net.

Think of the net proceeds as the selling price minus the broker’s commission (5% of the price) and minus the closing costs. If the selling price is P, the net is P minus 0.05P minus 1,150, which is 0.95P minus 1,150.

Set this equal to the target net of 47,300:

0.95P − 1,150 = 47,300

0.95P = 48,450

P = 48,450 ÷ 0.95 = 51,000

So the property must sell for 51,000 to net 47,300. Checking: 5% of 51,000 is 2,550; subtracting 2,550 and 1,150 from 51,000 leaves 47,300. Lower prices would yield a smaller net.