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Chapter 7: Problem 49

Solve. Your purchase price is \(\$ 68\) and the sales tax rate is \(9.5 \%\). Round each amount and use the rounded amounts to estimate the total price. Choose the best estimate. a. \(\$ 105\) b. \(\$ 58\) c. \(\$ 93\) d. \(\$ 77\)

Short Answer

Expert verified
The best estimate is $77 (option d).

Step by step solution

01

Estimate the Purchase Price

Round the purchase price of $68 to the nearest ten dollars. Since $68 is closer to $70, we round it to $70.
02

Estimate the Sales Tax Rate

The sales tax rate is given as 9.5%. For easier estimation, round this to the nearest whole percentage. 9.5% rounds up to 10%.
03

Calculate Estimated Sales Tax

Estimate the sales tax by calculating 10% of the rounded purchase price. 10% of \(70 is calculated as follows: \(0.10 \times 70 = 7\). So, the estimated sales tax is \)7.
04

Calculate the Estimated Total Price

Add the estimated sales tax to the rounded purchase price to find the total estimated price. This is calculated as \(70 + 7 = 77\).
05

Choose the Best Estimate

Compare the result from Step 4 to the options provided. The option closest to our estimated total price of $77 is option (d) $77.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rounding Numbers
Rounding numbers is an essential skill in mathematics, used to simplify numbers and make calculations easier. When rounding to the nearest ten, we look at the digit in the ones place. If this digit is 5 or higher, we round the number up. If it is lower, we round down. For example, in this exercise, the number 68 is rounded to 70 because 8 is greater than 5. This approach helps in estimating without losing significant precision, especially useful in scenarios like budgeting or quick mental calculations.
Percentage Calculation
Percentage calculation is a fundamental concept when working with proportions and comparisons in mathematics. It involves expressing a number as a fraction of 100. In practical terms, percentages are used to determine parts of a whole, such as calculating discounts or taxes. For instance, calculating 10% of a number involves multiplying by 0.10. Using percentages helps in understanding and solving problems related to growth, loss, and rates. In our example, rounding 9.5% to 10% simplifies the calculation while still providing a reliable estimate. It's a helpful tool to approximate outcomes efficiently.
Sales Tax Calculation
Sales tax calculation is a real-life application of percentage calculation, used to determine how much tax is added to a purchase based on a percentage rate. This is essential when estimating the final cost of an item after tax. For instance, if the sales tax rate is 9.5%, rounding it to 10% aids in easier calculations. To calculate the sales tax, multiply the rounded purchase price by the tax rate: in this scenario, 10% of 70 equals 7. Adding this tax to the item's price estimates the total cost, ensuring buyers can prepare financially. It's an everyday application of math in financial planning.

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Most popular questions from this chapter

Write the percent from the circle graph as a decimal and a fraction. Africa: \(16.2 \%\)

Add or subtract the fractions. $$3 \frac{1}{2}-\frac{11}{30}$$

In your own words, explain how to write a decimal as a percent.

Check the Chapter Opener bar graph. If the number of Internet users in 2016 was \(46.1 \%\) of the world population, it does not necessarily mean that each country of the world has \(46.1 \%\) of its population identified as Internet users. In fact, there is a country that claims to have \(100 \%\) of its population as Internet users. In the table below, we have listed a few selected countries along with Internet user data. Use your knowledge of percent and fill in the table. If needed, round percents to the nearest tenth and populations to the nearest hundred. (Source: Internet Live Stats) $$\begin{array}{|l|c|c|c|}\hline \text { Country } & \text { Population } & \begin{array}{c}\text { Internet Users % } \\\\\text { of Population }\end{array} & \begin{array}{c}\text { Number of } \\\\\text { Internet Users }\end{array} \\\\\hline \text { Ecuador} & & 43.1 \% & 7,055,575 \\\\\hline\end{array}$$

Explain what errors were made by each student when solving percent of increase or decrease problems and then correct the errors. See the Concept Checks in this section. "The population of a certain rural town was 150 in 1990, 180 in 2000, and 150 in 2010." Find the percent of increase in population from 1990 to 2000 . Miranda's solution: Percent of increase \(=\frac{30}{180}=0.1 \overline{6} \approx 16.7 \%\)
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