A car normally sells for $20,000 is on sale for $16,000. The sales tax is 7.5%.
What percent of the original price of the car is the final price?
The Correct answer and Explanation is:
The car originally costs $20,000, and after a discount, it sells for $16,000. To find the final price, including sales tax, we need to calculate the 7.5% sales tax on the discounted price of $16,000.
Step 1: Calculate the sales tax.
The sales tax is 7.5% of $16,000. To find this:Sales tax=16,000×7.5100=16,000×0.075=1,200\text{Sales tax} = 16,000 \times \frac{7.5}{100} = 16,000 \times 0.075 = 1,200Sales tax=16,000×1007.5=16,000×0.075=1,200
So, the sales tax is $1,200.
Step 2: Calculate the final price.
The final price of the car, after adding the sales tax, is:Final price=16,000+1,200=17,200\text{Final price} = 16,000 + 1,200 = 17,200Final price=16,000+1,200=17,200
Step 3: Find the percentage of the original price.
Now, we need to determine what percent of the original price ($20,000) the final price ($17,200) is. To do this, we use the formula for percentage:Percent of original price=(Final priceOriginal price)×100\text{Percent of original price} = \left( \frac{\text{Final price}}{\text{Original price}} \right) \times 100Percent of original price=(Original priceFinal price)×100
Substitute the values:Percent of original price=(17,20020,000)×100=0.86×100=86%\text{Percent of original price} = \left( \frac{17,200}{20,000} \right) \times 100 = 0.86 \times 100 = 86\%Percent of original price=(20,00017,200)×100=0.86×100=86%
Conclusion:
The final price of the car, after applying the discount and the sales tax, is 86% of the original price.
Explanation:
When calculating percentages in real-life scenarios, it’s important to understand the difference between the original cost, discounted price, and how taxes are applied. In this case, the $16,000 price tag reflects a discount from the original $20,000 price. Once the sales tax is added, the total cost becomes $17,200. By comparing this total cost to the original price, you can determine that the final price is 86% of the original price. This kind of calculation is useful for understanding how discounts and taxes affect the overall cost of a purchase.