1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 4.7 Applications: Discount, Sales Tax, Commission, and Percent Increase/Decrease

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Learn Polya’s four-step process for problem solving. o Understand how to calculate a discount. o Understand how to calculate sales tax. o Understand how to calculate commission. o Understand how to calculate percent increase and percent decrease.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. The Problem Solving Process Basic Steps for Solving Word Problems 1.Understand the problem. For example, a.Read the problem. b.Understand all the words. c.If it helps, restate the problem in your own words. d.Be sure that there is enough information.

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. The Problem Solving Process Basic Steps for Solving Word Problems (cont.) 2.Devise a plan using, for example, one or all of the following: a.Guess, estimate, or make a list of possibilities. b.Draw a picture or diagram. c.Use a variable and form an equation.

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. The Problem Solving Process Basic Steps for Solving Word Problems (cont.) 3.Carry out the plan. For example, a.Try all the possibilities you have listed. b.Study your picture or diagram for insight into the solution. c.Solve any equation that you may have set up.

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. The Problem Solving Process Basic Steps for Solving Word Problems (cont.) 4.Look back over the results. For example, a.Can you see an easier way to solve the problem? b.Does your solution actually work? Does it make sense in terms of the wording of the problem? Is it reasonable? c.If there is an equation, check your answer in the equation.

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Solving Discount Problems A refrigerator that regularly sells for $1200 is on sale at a 20% discount. a. What is the amount of the discount? Solution To find the discount, we find 20% of $1200. 20% of $1200 is _____

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. The discount is $240. Example 1: Solving Discount Problems (cont.)

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Solving Discount Problems (cont.) b. What is the sale price? Solution Find the sale price by subtracting the discount from the original price.

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Solving Discount Problems Large fluffy towels were on sale at a discount of 30%. If the sale price was $8.40, what was the original price? Solution In this case, we already know the sale price. Now, we need to reason that because the discount was 30%, the sale price represents 70% of the original price. (100% − 30% = 70%) Also, note that the original price will be more than the sale price of $8.40. 70% of _____ is $8.40.

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Solving Discount Problems (cont.) The original price of the towels was $12.00 each.

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Solving Sales Tax Problems If the sales tax rate is 6%, what would be the final cost of a laptop computer priced at $899? Solution First, find the sales tax by taking 6% of $899. 6% of 899 is _____

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Solving Sales Tax Problems (cont.)

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Next, find the final cost by adding the sales tax to the original price. The final cost of the laptop would be $952.94. Example 3: Solving Sales Tax Problems (cont.)

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Solving Commission Problems Susan sells women’s shoes. She earns a salary of $2000 a month plus a commission of 8% on what she sells over $8500. What did Susan earn the month she sold $22,500 worth of shoes? Solution First, find the base for her commission by subtracting $8500 from her sales.

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Solving Commission Problems (cont.) Next, find the amount of the commission by taking 8% of $14,000.

17. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Solving Commission Problems (cont.) Finally, add her salary and the amount of the commission to find what she earned. Susan earned $3120 for the month.

18. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Now determine the percent increase by finding what percent 8 is of 80. Use 80 as the base because it is the number that was increased. Example 5: Finding the Percent Increase Ben’s last two exam scores in algebra were 80 and 88. What was the percent increase from the first exam to the second? Solution First, find the increase in score from the first exam to the second.

19. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. So Ben’s score increased by 10%. Example 5: Finding the Percent Increase (cont.)

20. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Finding the Percent Decrease Three years ago you bought a new car for $25,000. Your business is doing well and you are now looking for another new car and want to trade in your first car. The dealer has told you that the trade in value of your car in now $17,500. What is the percent decrease in the value of your car?

21. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Solution First find the actual decrease in the value: Now we find the percent decrease by finding what percent $7500 (the decrease) is of $25,000 (the base price). Example 6: Finding the Percent Decrease

22. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Finding the Percent Decrease (cont.) So the percent decrease in the value of your car is 30%.

23. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems 1.A television which normally sells for $300 is priced at a 10% discount. Find a. the amount of the discount and b. the sale price. 2.If the sales tax rate is 6.5%, what is the tax on an $800 purchase? 3.A realtor works on a 5% commission. What would be her commission on a house that sold for $485,000?

24. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. 4.Central Valley Community College had 48 teams compete at their 1st annual corn hole tournament. The following year they had 54 teams compete. What was the percent increase in competing teams? Practice Problems (cont.)

25. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers 1.a. $30b. 270 2.$52 3.$24,250 4.12.5%