PREALGEBRA
PREALGEBRA
15th Edition
ISBN: 9781938168994
Author: OpenStax
Publisher: OpenStax
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Concept explainers

Estimation
A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.
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Chapter 6.5, Problem 6.98TI

:: 6.98 Translate to a proportion: 27 is 36% of what number?

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Chapter 6 Solutions

PREALGEBRA

Ch. 6.1 - TRY IT :: 6.1 Write the percent as a ratio....Ch. 6.1 - TRY IT :: 6.1 Write the percent as a ratio. A...Ch. 6.1 - TRY IT:: 6.3 Write as a ratio and then as a...Ch. 6.1 - TRY IT :: 6.4 Write as a ratio and then as a...Ch. 6.1 - TRY IT :: 6.5 Convert each percent to a fraction:...Ch. 6.1 - TRY IT :: 6.6 Convert each percent to a fraction:...Ch. 6.1 - TRY IT :: 6.7 Convert each percent to a fraction:...Ch. 6.1 - TRY IT :: 6.7 Convert each percent to a fraction:...Ch. 6.1 - TRY IT :: 6.9 Convert each percent to a fraction:...Ch. 6.1 - TRY IT :: 6.10 Convert each percent to a decimal:...
Ch. 6.1 - TRY IT :: 6.11 Convert each percent to a decimal:...Ch. 6.1 - TRY IT :: 6.12 Convert each percent to a decimal:...Ch. 6.1 - TRY IT :: 6.13 Convert the percent to: (a) a...Ch. 6.1 - TRY IT :: 6.14 Convert the percent to: (a) a...Ch. 6.1 - TRY IT :: 6.15 Convert the percent to: (a) a...Ch. 6.1 - TRY IT :: 6.16 Convert the percent to: (a) a...Ch. 6.1 - TRY IT :: 6.17 Convert each decimal to a percent:...Ch. 6.1 - TRY IT :: 6.18 Convert each decimal to a percent:...Ch. 6.1 - TRY IT :: 6.19 Convert each decimal to a percent:...Ch. 6.1 - TRY IT :: 6.20 Convert each decimal to a percent:...Ch. 6.1 - TRY IT :: 6.21 Convert each fraction or mixed...Ch. 6.1 - TRY IT :: 6.23 Convert each fraction or mixed...Ch. 6.1 - TRY IT :: 6.23 Convert the fraction to a percent:...Ch. 6.1 - TRY IT :: 6.24 Convert the fraction to a percent:...Ch. 6.1 - TRY IT :: 6.25 Convert the fraction to a percent:...Ch. 6.1 - TRY IT :: 6.26 Convert the fraction to a percent:...Ch. 6.1 - Use the Definition of Percents In the following...Ch. 6.1 - Use the Definition of Percents. In the following...Ch. 6.1 - Use the Definition of Percents In the following...Ch. 6.1 - Use the Definition of Percents In the following...Ch. 6.1 - Use the Definition of PercentsIn the following...Ch. 6.1 - Use the Definition of Percents In the following...Ch. 6.1 - Use the Definition of Percents In the following...Ch. 6.1 - Use the Definition of Percents In the following...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - 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Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Percents to Fractions and Decimals In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - SConvert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimal and Fractions to Presents In the...Ch. 6.1 - Convert Decimal and Fractions to Presents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents In the...Ch. 6.1 - Convert Decimals and Fractions to Percents Sales...Ch. 6.1 - Savings Ryan has 25% of each paycheck...Ch. 6.1 - Amelio is shopping for textbooks online. He found...Ch. 6.1 - Convert Decimals and Fractions to Percents Write...Ch. 6.1 - Convert Decimals and Fractions to Percents Write...Ch. 6.1 - Convert Decimals and Fractions to Percents 92....Ch. 6.1 - Convert Decimals and Fractions to Percents 93....Ch. 6.1 - Convert 25%, 50%, 75%, and 100% to fractions. Do...Ch. 6.1 - Convert 110,210,310,410,510,610,710,810 , and 910...Ch. 6.1 - When the Szetos sold their home, the selling price...Ch. 6.1 - According to cnn.com, cell phone use in 2008 was...Ch. 6.2 - TRY IT :: 6.27 What number is 45% of 80?Ch. 6.2 - TRY IT :: 6.28 What number is 525% of 60?Ch. 6.2 - TRY IT :: 6.29 of 78 is what number?Ch. 6.2 - TRY IT :: 6.30 of 72 is what number?Ch. 6.2 - TRY IT :: 6.31 17 is 25% of what number?Ch. 6.2 - TRY IT :: 6.32 40 is 62.5% of what number?Ch. 6.2 - TRY IT :: 6.33 of what number is $1.95?Ch. 6.2 - TRY IT :: 6.34 8.5% of what number is $3,06?Ch. 6.2 - TRY IT :: 6.35 What percent of 76 is 57?Ch. 6.2 - TRY IT :: 6.36 What percent of 120 is 96?Ch. 6.2 - TRY IT :: 6.37 is what percent of 88?Ch. 6.2 - TRY IT :: 6.38 what percent of 72?Ch. 6.2 - TRY IT :: 6.39 Cierra and her sister enjoyed a...Ch. 6.2 - TRY IT :: 6.40 Kimngoc had lunch at her favorite...Ch. 6.2 - TRY IT :: 6.41 One serving of wheat square cereal...Ch. 6.2 - TRY IT :: 6.42 One serving of rice cereal has 190...Ch. 6.2 - TRY IT :: 6.43 Veronica is planning to make...Ch. 6.2 - TRY IT :: 6.44 The brownie mix Ricardo plans to...Ch. 6.2 - TRY IT :: 6.45 In 2011, the IRS increased the...Ch. 6.2 - TRY IT :: 6.46 In 1995, the standard bus fare in...Ch. 6.2 - TRY IT :: 6.47 The population of one city was...Ch. 6.2 - TRY IT :: 6.48 Last year Sheila’s salary was...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Translate and Solve Basic Percent Equations In the...Ch. 6.2 - Solve Applications of Percents In the following...Ch. 6.2 - Solve Applications of Percents In the following...Ch. 6.2 - Solve Applications of Percents In the following...Ch. 6.2 - Solve Applications of Percents In the following...Ch. 6.2 - Solve Applications of Percents In the following...Ch. 6.2 - Solve Applications of Percents In the following...Ch. 6.2 - Solve Applications of Percents In the following...Ch. 6.2 - Solve Applications of Percents In the following...Ch. 6.2 - Solve Applications of Percents In the following...Ch. 6.2 - Solve Applications of Percents In the following...Ch. 6.2 - Solve Applications of Percents In the following...Ch. 6.2 - Solve Applications of Percents In the following...Ch. 6.2 - Solve Applications of Percents In the following...Ch. 6.2 - Solve Applications of Percents In the following...Ch. 6.2 - Solve Applications of Percents In the following...Ch. 6.2 - Solve Applications of Percents In the following...Ch. 6.2 - Find the percent increase and percent Decrease In...Ch. 6.2 - Find the percent increase and percent Decrease In...Ch. 6.2 - Find the percent increase and percent Decrease In...Ch. 6.2 - Find the percent increase and percent Decrease In...Ch. 6.2 - Find the percent increase and percent Decrease In...Ch. 6.2 - Find the percent increase and percent Decrease In...Ch. 6.2 - Find the percent increase and percent Decrease In...Ch. 6.2 - Find the percent increase and percent Decrease In...Ch. 6.2 - Find the percent increase and percent Decrease In...Ch. 6.2 - Find the percent increase and percent Decrease In...Ch. 6.2 - Find the percent increase and percent Decrease In...Ch. 6.2 - Find the percent increase and percent Decrease In...Ch. 6.2 - Find the percent increase and percent Decrease In...Ch. 6.2 - Find the percent increase and percent Decrease In...Ch. 6.3 - TRY IT:: 6.49 Find (a) the sales tax and (b) the...Ch. 6.3 - TRY IT:: 6.50 Find (a) the sales tax and (b) the...Ch. 6.3 - TRY IT:: 6 51 Diego bought a new car for $26,525....Ch. 6.3 - TRY IT:: 6.52 What is the sales tax rate if a...Ch. 6.3 - TRY IT :: 6.53 Bob is a travel agent He receives...Ch. 6.3 - TRY IT:: 6 54 Fernando receives 18% commission...Ch. 6.3 - TRY IT:: 6.55 Homer received $1,140 commission...Ch. 6.3 - TRY IT :: 6.56 Marta bought a dishwasher that was...Ch. 6.3 - TRY IT :: 6.57 Marta bought a dishwasher that was...Ch. 6.3 - TRY IT :: 6.58 Orlando bought a pair of shoes that...Ch. 6.3 - TRY IT :: 6.59 Find (a) the amount of discount and...Ch. 6.3 - TRY IT:: 6.60 Find (a) the amount of discount and...Ch. 6.3 - TRY IT :: 6.61 Find (a) the amount of discount and...Ch. 6.3 - TRY IT :: 6.62 Find (a) the amount of discount and...Ch. 6.3 - TRY IT:: 6 63 Jim's music store bought a guitar at...Ch. 6.3 - TRY IT :: 6.64 The Auto Resale Store bought...Ch. 6.3 - Solve Sales Tax Applications In the following...Ch. 6.3 - Solve Sales Tax Applications In the following...Ch. 6.3 - Solve Sales Tax Applications In the following...Ch. 6.3 - Solve Sales Tax Applications In the following...Ch. 6.3 - Solve Sales Tax Applications In the following...Ch. 6.3 - Solve Sales Tax Applications In the following...Ch. 6.3 - Solve Sales Tax Applications In the following...Ch. 6.3 - Solve Sales Tax Applications In the following...Ch. 6.3 - In the following exercises, find the sales tax...Ch. 6.3 - In the following exercises, find the sales tax...Ch. 6.3 - In the following exercises, find the sales tax...Ch. 6.3 - In the following exercises, find the sales tax...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Commission Applications In the following...Ch. 6.3 - Solve Discount Applications In the following...Ch. 6.3 - Solve Discount Applications In the following...Ch. 6.3 - Solve Discount Applications In the following...Ch. 6.3 - Solve Discount Applications In the following...Ch. 6.3 - Solve Discount Applications In the following...Ch. 6.3 - Solve Discount Applications In the following...Ch. 6.3 - Solve Discount Applications In the following...Ch. 6.3 - Solve Mark-up Applications In the following...Ch. 6.3 - Solve Mark-up Applications In the following...Ch. 6.3 - Solve Mark-up Applications In the following...Ch. 6.3 - Solve Mark-up Applications In the following...Ch. 6.3 - Solve Mark-up Applications In the following...Ch. 6.3 - Solve Mark-up Applications In the following...Ch. 6.3 - Solve Mark-up Applications In the following...Ch. 6.3 - Solve Mark-up Applications In the following...Ch. 6.3 - Solve Mark-up Applications In the following...Ch. 6.4 - TRY IT:: 6 65 Find the simple interest earned...Ch. 6.4 - TRY IT:: 6 66 Find the simple interest earned...Ch. 6.4 - TRY IT:: 6.67 Find the principal invested if $495...Ch. 6.4 - TRY IT :: 6.68 Find the principal invested if...Ch. 6.4 - TRY IT:: 6.69 Find the rate if a principal of...Ch. 6.4 - TRY IT ::6.70 Find the rate if a principal of...Ch. 6.4 - TRY IT:: 6.71 Areli invested a principal of $950...Ch. 6.4 - TRY IT:: 6.72 Susana invested a principal of...Ch. 6.4 - TRY IT :: 6.73 Jim lent his sister $5,000 to help...Ch. 6.4 - TRY IT :: 674 Hang borrowed $7,500 from her...Ch. 6.4 - TRY IT:: 6 75 Sean's new car loan statement said...Ch. 6.4 - TRY IT:: 6 76 In 5 years, Gloria's bank account...Ch. 6.4 - TRY IT:: 6 77 Adriana invested $4,500 for 8 months...Ch. 6.4 - TRY IT:: 6.78 Milton invested $2,460 for 20 months...Ch. 6.4 - Use the Simple Interest Formula In the following...Ch. 6.4 - Use the Simple Interest Formula In the following...Ch. 6.4 - Use the Simple Interest Formula In the following...Ch. 6.4 - Use the Simple Interest Formula In the following...Ch. 6.4 - Use the Simple Interest Formula In the following...Ch. 6.4 - Use the Simple Interest Formula In the following...Ch. 6.4 - In the following exercises, solve the problem...Ch. 6.4 - In the following exercises, solve the problem...Ch. 6.4 - In the following exercises, solve the problem...Ch. 6.4 - In the following exercises, solve the problem...Ch. 6.4 - In the following exercises, solve the problem...Ch. 6.4 - In the following exercises, solve the problem...Ch. 6.4 - In the following exercises, solve the problem...Ch. 6.4 - In the following exercises, solve the problem...Ch. 6.4 - In the following exercises, solve the problem...Ch. 6.4 - 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Solve Simple Interest Applications In the...Ch. 6.4 - Solve Simple Interest Applications In the...Ch. 6.4 - Solve Simple Interest Applications In the...Ch. 6.4 - Solve Simple Interest Applications In the...Ch. 6.4 - Solve Simple Interest Applications In the...Ch. 6.4 - Solve Simple Interest Applications In the...Ch. 6.4 - Solve Simple Interest Applications In the...Ch. 6.4 - Solve Simple Interest Applications In the...Ch. 6.4 - Solve Simple Interest Applications In the...Ch. 6.5 - TRY IT:: 6.79 Write each sentence as a proportion:...Ch. 6.5 - TRY IT :: 6.80 Write each sentence as a...Ch. 6.5 - TRY IT :: 6.81 Determine whether each equation is...Ch. 6.5 - TRY IT :: 6.82 Determine whether each equation is...Ch. 6.5 - TRY IT :: 6.83 Solve the proportion: n84=1112 .Ch. 6.5 - TRY IT :: 6.84 Solve the proportion: y96=1312 .Ch. 6.5 - TRY IT :: 6.85 Solve the proportion: 91b=75 .Ch. 6.5 - TRY IT :: 6.86 Solve the proportion: 39c=138 .Ch. 6.5 - TRY IT :: 6.87 Solve the proportion: 8498=6x .Ch. 6.5 - TRY IT :: 6.88 Solve the proportion: 7y=105135 .Ch. 6.5 - Try IT :: 6.89 Pediatricians prescribe 5...Ch. 6.5 - TRY IT :: 6.90 For every 1 kilogram (kg) of a...Ch. 6.5 - TRY IT :: 6.91 Marissa loves the Caramel Macchiato...Ch. 6.5 - TRY IT :: 6.92 Yaneli loves Starburst candies, but...Ch. 6.5 - TRY IT :: 6.93 Yurianna is going to Europe and...Ch. 6.5 - TRY IT :: 6.94 Corey and Nicole are traveling to...Ch. 6.5 - TRY IT :: 6.95 Translate to a proportion: What...Ch. 6.5 - TRY IT :: 6.96 Translate to a proportion: What...Ch. 6.5 - TRY IT :: 6.97 Translate to a proportion: 36 is...Ch. 6.5 - :: 6.98 Translate to a proportion: 27 is 36% of...Ch. 6.5 - TRY IT :: 6.99 Translate to a proportion: What...Ch. 6.5 - TRY IT :: 6,100 Translate to a proportion: What...Ch. 6.5 - TRY IT:: 6.101 Translate and solve using...Ch. 6.5 - TRY IT:: 6.102 Translate and solve using...Ch. 6.5 - TRY IT:: 6.103 Translate and solve using...Ch. 6.5 - TRY IT:: 6.104 Translate and solve using...Ch. 6.5 - TRY IT:: 6.103 Translate and solve using...Ch. 6.5 - TRY IT:: 6.106 Translate and solve using...Ch. 6.5 - TRY IT:: 6.107 Translate and solve using...Ch. 6.5 - TRY IT :: 6.108 Translate and solve using...Ch. 6.5 - Use the Definition of Proportion In the following...Ch. 6.5 - Use the Definition of Proportion In the following...Ch. 6.5 - Use the Definition of Proportion In the following...Ch. 6.5 - Use the Definition of Proportion In the following...Ch. 6.5 - Use the Definition of Proportion In the following...Ch. 6.5 - Use the Definition of Proportion In the following...Ch. 6.5 - Use the Definition of Proportion In the following...Ch. 6.5 - Use the Definition of Proportion In the following...Ch. 6.5 - Use the Definition of Proportion In the following...Ch. 6.5 - Use the Definition of Proportion In the following...Ch. 6.5 - Use the Definition of Proportion In the following...Ch. 6.5 - Use the Definition of Proportion In the following...Ch. 6.5 - In the following exercises, determine whether each...Ch. 6.5 - In the following exercises, determine whether each...Ch. 6.5 - 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Solve Sales Tax, Commission, and Discount...Ch. 6 - Solve Sales Tax, Commission, and Discount...Ch. 6 - Solve Sales Tax, Commission, and Discount...Ch. 6 - Solve Sales Tax, Commission, and Discount...Ch. 6 - Solve Sales Tax, Commission, and Discount...Ch. 6 - Solve Sales Tax, Commission, and Discount...Ch. 6 - Solve Sales Tax, Commission, and Discount...Ch. 6 - Solve Sales Tax, Commission, and Discount...Ch. 6 - Solve Sales Tax, Commission, and Discount...Ch. 6 - Solve Sales Tax, Commission, and Discount...Ch. 6 - Solve Simple Interest Applications In the...Ch. 6 - Solve Simple Interest Applications In the...Ch. 6 - Solve Simple Interest Applications In the...Ch. 6 - Solve Simple Interest Applications In the...Ch. 6 - Solve Simple Interest Applications In the...Ch. 6 - Solve Simple Interest Applications In the...Ch. 6 - Solve Simple Interest Applications In the...Ch. 6 - Solve Simple Interest Applications In the...Ch. 6 - Solve Proportions and their Applications In the...Ch. 6 - Solve Proportions and their Applications In the...Ch. 6 - 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