In a price problem, the last step is to divide the net to be received by the decimal found in step 2. If the net to be received is $75,000 and the decimal from step 2 is 0.75, what is the final price?

In a price problem, the last step is to divide the net to be received by the decimal found in step 2. If the net to be received is $75,000 and the decimal from step 2 is 0.75, what is the final price?

• A. $100,000
• B. $75,000
• C. $125,000
• D. $150,000

Answer: (A)

When the net amount represents a percentage of the final price, you recover the full price by dividing the net by that percentage. Here, 75% of the final price is the net received: 0.75 × Final Price = 75,000. Let the final price be P. Then 0.75P = 75,000, so P = 75,000 ÷ 0.75. Calculating gives 100,000. You can also see this by noting 0.75 equals 3/4, so dividing by 3/4 is the same as multiplying by 4/3: 75,000 × 4/3 = 100,000. Verify: 0.75 × 100,000 = 75,000. Therefore, the final price is $100,000.

When the net amount represents a percentage of the final price, you recover the full price by dividing the net by that percentage. Here, 75% of the final price is the net received: 0.75 × Final Price = 75,000. Let the final price be P. Then 0.75P = 75,000, so P = 75,000 ÷ 0.75. Calculating gives 100,000. You can also see this by noting 0.75 equals 3/4, so dividing by 3/4 is the same as multiplying by 4/3: 75,000 × 4/3 = 100,000. Verify: 0.75 × 100,000 = 75,000. Therefore, the final price is $100,000.