/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 15 A new coat costs \(\$ 68.25 .\) ... [FREE SOLUTION] | 91影视

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Chapter 7: Problem 15

A new coat costs \(\$ 68.25 .\) If the sales tax rate is \(5 \%\), what is the total bill?

Short Answer

Expert verified
The total bill is \(\$71.66\).

Step by step solution

01

Understand the Problem

The total bill includes the cost of the coat plus the sales tax. The coat costs \(\$68.25\) and the sales tax rate is \(5\%\).
02

Calculate the Sales Tax

To find the sales tax, multiply the cost of the coat by the tax rate. The formula is: \[\text{Sales Tax} = \text{Coat Cost} \times \text{Tax Rate}\] \(= 68.25 \times 0.05 = 3.4125\)
03

Round the Sales Tax

Sales tax is usually rounded to the nearest cent. Therefore, round \(3.4125\) to \(3.41\).
04

Calculate the Total Bill

Add the cost of the coat and the rounded sales tax: \[\text{Total Bill} = 68.25 + 3.41 = 71.66\]

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Key Concepts

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

Percentage
Understanding percentages is crucial for calculating sales tax. A percentage is a way of expressing a number as a fraction of 100. So, when the problem states that the sales tax rate is 5%, it means for every \(100 spent, you pay \)5 in tax. To convert a percentage to a decimal for calculations, simply divide by 100. For instance, 5% becomes 0.05. This conversion helps easily multiply percentages with other numbers.
Rounding
Rounding numbers makes them simpler and easier to work with. In the context of sales tax, rounding usually happens to the nearest cent because money is typically dealt with in two decimal places. For example, if a calculation results in 3.4125, you round it to 3.41. Rounding involves looking at the digit after the place value you are rounding to; if it's 5 or greater, you round up, and if it's less than 5, you round down.
Total Cost Calculation
To determine the total cost, you need to add the original price of the item to the calculated sales tax. Begin by calculating the sales tax, then round it to the nearest cent. Finally, add this rounded tax amount to the original price of the item. In our example, the coat costs \(\text{68.25}\), and after finding the rounded tax as \(\text{3.41}\), the total bill is \(\text{71.66}\).
Step by Step Solution
Breaking problems down into steps can simplify complex tasks. Here鈥檚 a simple approach: recognize the components of the problem, apply the needed formulas, perform intermediate calculations, and combine results. For the coat exercise, we followed these steps: identified the need to add sales tax, calculated the tax as \(\text{3.4125}\), rounded it to \(\text{3.41}\), and added this to the coat鈥檚 price to find the total bill of \(\text{71.66}\). This structured method ensures each part of the problem is handled methodically and accurately.

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Most popular questions from this chapter

Find the total amount in an account for an investment subject to the following conditions. Principal $$\$ 9,000$$ Annual Interest Rate $$4 \%$$ Time, Years $$2 \frac{1}{2}$$ Compounded Quarterly Total Amount __________

Convert the fraction to a percent. $$\frac{5}{8}$$

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{8}{11}$$

Which of the numbers represent \(125 \% ?\) a. 1.25 b. 0.125 c. \(\frac{5}{4}\) d. \(\frac{5}{4} \%\)

Convert the decimal to a percent. $$0.0008$$
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