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 $99,000 and the decimal from step 2 is 0.99, 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 $99,000 and the decimal from step 2 is 0.99, what is the final price?

• A. $100,000
• B. $99,000
• C. $101,000
• D. $90,000

Answer: (A)

When you know the net amount received is a percentage (or decimal) of the final price, you recover the final price by dividing the net by that decimal, because net = final price × decimal. Here the decimal is 0.99, so the final price is 99,000 ÷ 0.99. Since 0.99 equals 99/100, this is 99,000 × (100/99) = 1,000 × 100 = 100,000. Check: 100,000 × 0.99 = 99,000, which matches the net. The final price is $100,000.

When you know the net amount received is a percentage (or decimal) of the final price, you recover the final price by dividing the net by that decimal, because net = final price × decimal. Here the decimal is 0.99, so the final price is 99,000 ÷ 0.99. Since 0.99 equals 99/100, this is 99,000 × (100/99) = 1,000 × 100 = 100,000. Check: 100,000 × 0.99 = 99,000, which matches the net. The final price is $100,000.