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 $150,000 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 $150,000 and the decimal from step 2 is 0.75, what is the final price?

• A. $200,000
• B. $150,000
• C. $160,000
• D. $180,000

Answer: (A)

When you have a net amount and you know what percent of the final price that net represents, you recover the full price by dividing the net by that percent (as a decimal). Here, the net to receive is 150,000 and the decimal from the step is 0.75, meaning you receive 75% of the final price. So the final price = 150,000 ÷ 0.75. Calculating, 0.75 is 3/4, so dividing by 3/4 is the same as multiplying by 4/3: 150,000 × 4/3 = 150,000 ÷ 3 × 4 = 50,000 × 4 = 200,000. You can check this by restoring the net: 200,000 × 0.75 = 150,000. Only the price that yields a net of 150,000 when multiplied by 0.75 is 200,000, since the other options would produce nets clearly not equal to 150,000. Therefore, the final price is 200,000 dollars.

When you have a net amount and you know what percent of the final price that net represents, you recover the full price by dividing the net by that percent (as a decimal). Here, the net to receive is 150,000 and the decimal from the step is 0.75, meaning you receive 75% of the final price. So the final price = 150,000 ÷ 0.75.

Calculating, 0.75 is 3/4, so dividing by 3/4 is the same as multiplying by 4/3: 150,000 × 4/3 = 150,000 ÷ 3 × 4 = 50,000 × 4 = 200,000. You can check this by restoring the net: 200,000 × 0.75 = 150,000.

Only the price that yields a net of 150,000 when multiplied by 0.75 is 200,000, since the other options would produce nets clearly not equal to 150,000. Therefore, the final price is 200,000 dollars.