1. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems: Prealgebra Section 6.4: Applications: Discount, Sales Tax, Commission, Profit, and Tipping

2. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Objectives o Become familiar with the problem solving process. o Learn the meaning of the terms discount and sales tax and be able to calculate these values. o Understand the concept of commission, profit, and percent of profit and be able to solve problems related to these concepts. o Know how to calculate a tip for a service.

3. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Basic Steps for Solving Word Problems 1. Understand the problem. 2. Devise a plan. 3. Carry out the plan. 4. Look back over the results. Obj 1: Problem Solving Process

4. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Obj 2: Discount and Sales Tax o To attract customers or to sell goods that have been in stock for some time, retailers and manufacturers offer a discount, a reduction in the original selling price. The new, reduced price is called the sale price, and the discount is the difference between the original price and the sale price. The rate of discount (or percent of discount) is a percent of the original price. o Discounts are sometimes advertised as a percent “off” the selling price.

5. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Terms Related to Discount and Sales Tax Discount:Reduction in original selling price Sale Price:Original selling price minus the discount Rate of Discount:Percent of original price to be discounted Sales Tax:Tax based on actual selling price Rate of Sales Tax:Percent of actual selling price Obj 2: Discount and Sales Tax (cont.)

6. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 1: Discount and Sales Tax A new refrigerator that regularly sells for $1200 is on sale at a 20% discount. a. What is the amount of the discount? b. What is the sale price? Solution Step 1: Read the problem carefully. Do you understand all the words? Step 2: Make a plan. The plan here is a. find the amount of the discount, then b. subtract this amount from the original price to find the sale price. Step 3: Carry out the plan. Step 4: Check to see that the answer makes sense.

7. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 1: Discount and Sales Tax (cont.) A new refrigerator that regularly sells for $1200 is on sale at a 20% discount. a. What is the amount of the discount? b. What is the sale price? Solution a. Find the discount: 20% of $1200 is _____. The discount is $240.00. b. Find the sale price. Subtract the discount from the original price. The sale price is $960.00.

8. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 2: Discount and Sales Tax If sales tax is calculated at of the sale price, what is the final cost of the refrigerator? Solution Step 1: Read the problem carefully. Step 2: Make a plan. The plan here is to find the sales tax and then add the sales tax to the sale price to find the final cost. Step 3: Carry out the plan. Step 4: Check to see that the answer is reasonable.

9. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 2: Discount and Sales Tax (cont.) If sales tax is calculated at of the sale price, what is the final cost of the refrigerator? Solution a. Find the amount of the sales tax: The sales tax is $69.60. b. From experience, we know to add tax to the sales price to find the final cost. The final cost of the refrigerator is $1029.60.

10. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 1: Discount and Sales Tax A new front load washing machine that regularly sells for $880 is on sale at a 30% discount. a. What is the amount of the discount? b. What is the sale price? Solution Step 1: Read the problem carefully. Do you understand all the words? Step 2: Make a plan. The plan here is a. find the amount of the discount, then b. subtract this amount from the original price to find the sale price. Step 3: Carry out the plan. Step 4: Check to see that the answer makes sense.

11. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 1: Discount and Sales Tax (cont.) A new front load washing machine that regularly sells for $880 is on sale at a 30% discount. a. What is the amount of the discount? b. What is the sale price? Solution a. Find the discount: 30% of $880 is _____. The discount is $264.00. b. Find the sale price. Subtract the discount from the original price. The sale price is $616.00.

12. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 2: Discount and Sales Tax If sales tax is calculated at, what is the final cost of the front load washing machine? Solution Step 1: Read the problem carefully. Step 2: Make a plan. The plan here is to find the sales tax and then add the sales tax to the sale price to find the final cost. Step 3: Carry out the plan. Step 4: Check to see that the answer is reasonable.

13. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 2: Discount and Sales Tax (cont.) If sales tax is calculated at, what is the final cost of the front load washing machine? Solution a. Find the amount of the sales tax: The sales tax is $27.72. b. From experience, we know to add tax to the sales price to find the final cost. The final cost of the front load washing machine is $643.72.

14. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 3: Discount and Sales Tax Large fluffy towels were on sale at a discount of 30%. If the sale price was $8.40, what was the original price? Solution Step 1: Read the problem carefully. Step 2: Make a plan. First realize we are not trying to find the discount. We already know the sale price. We need to realize that the sale price is 70% of the original price. (100% – 30% = 70%) Step 3: Carry out the plan. Set up the equation: 0.70B = 8.40 Step 4: Check to see that the answer makes sense.

15. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 3: Discount and Sales Tax (cont.) Large fluffy towels were on sale at a discount of 30%. If the sale price was $8.40, what was the original price? Solution The original price of the towels was $12.00 each.

16. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 3: Discount and Sales Tax Leather bean bag chairs are on sale at the local department store for $48.80. If this was a discount of 20%, what was the original price? Solution Step 1: Read the problem carefully. Step 2: Make a plan. First realize we are not trying to find the discount. We already know the sale price. We need to realize that the sale price is 80% of the original price. (100% – 20% = 80%) Step 3: Carry out the plan. Set up the equation: 0.80B = 48.80 Step 4: Check to see that the answer makes sense.

17. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 3: Discount and Sales Tax (cont.) Leather bean bag chairs are on sale at the local department store for $48.80. If this was a discount of 20%, what was the original price? Solution The original price of the bean bag chair was $61.00.

18. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Obj 3: Commissions A commission is a fee paid to an agent or salesperson for a service. Commissions are usually a percent of a negotiated contract or a percent of sales. In some cases, salespeople earn a straight commission on what they sell. In other cases, the salesperson earns a base salary plus a commission on sales above a certain level.

19. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 4: Commissions Susan earns a salary of $1100 a month plus a commission of 8% on whatever she sells after she has sold $8500 in merchandise. Her coworker sold $15,000 in merchandise. What did Susan earn the month she sold $22,500 in merchandise? Solution Step 1: Read the problem carefully. Step 2: Make a plan. Find the commission and add it to the salary. Remember, the commission is made only on the amount over $8500. Step 3: Carry out the plan. Find the base for the commission, multiply that base by 8%, and add the result to $1100. Step 4: Make sure the answer is reasonable.

20. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 4: Commissions (cont.) Susan earns a salary of $1100 a month plus a commission of 8% on whatever she sells after she has sold $8500 in merchandise. Her coworker sold $15,000 in merchandise. What did Susan earn the month she sold $22,500 in merchandise? Solution a. Find the base for her commission. Since the commission is based on what she sells over $8500, we subtract $8500 from her sales. $22,500 –8500 $14,000 Total sales Amount on which she does not earn a commission Base for commission

21. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 4: Commissions (cont.) Susan earns a salary of $1100 a month plus a commission of 8% on whatever she sells after she has sold $8500 in merchandise. Her coworker sold $15,000 in merchandise. What did Susan earn the month she sold $22,500 in merchandise? Solution She earned $2220 for the month. b. Now find the amount of the commission by finding 8% of the base. c.Add the amount of the commission to her salary to find her income for the month. $1100 +1120 $2220 Salary Commission Income for month

22. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 4: Commissions A salesperson earns a salary of $1500 a month plus a 10% commission on whatever he sells after he has sold $7700 in merchandise. What will the salesperson earn if he sold $11,000 of merchandise in one month? Solution Step 1: Read the problem carefully. Step 2: Make a plan. Find the commission and add it to the salary. Remember, the commission is made only on the amount over $7700. Step 3: Carry out the plan. Find the base for the commission, multiply that base by 10%, and add the result to $1500. Step 4: Make sure the answer is reasonable.

23. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 4: Commissions (cont.) A salesperson earns a salary of $1500 a month plus a 10% commission on whatever he sells after he has sold $7700 in merchandise. What will the salesperson earn if he sold $11,000 of merchandise in one month? Solution a. Find the base for his commission. Since the commission is based on what he sells over $7700, we subtract $7700 from his sales. $11,000 –7700 $3300 Total sales Amount on which he does not earn a commission Base for commission

24. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 4: Commissions (cont.) A salesperson earns a salary of $1500 a month plus a 10% commission on whatever he sells after he has sold $7700 in merchandise. What will the salesperson earn if he sold $11,000 of merchandise in one month? Solution He earned $1830 for the month. b. Now find the amount of the commission by finding 10% of the base. c. Add the amount of the commission to his salary to find his income for the month. $1500 + 330 $1830 Salary Commission Income for month

25. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Obj 3: Profit and Percent of Profit Manufacturers and retailers are concerned with the profit on each item produced or sold. In this sense, the profit on an item is the difference between the selling price to the customer and the cost to the company. The percent of profit is a ratio. And, as the following discussion indicates, this ratio can be based either on cost or on selling price.

26. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Terms Related to Profit Profit: The difference between selling price and cost. Profit = Selling Price – Cost Percent of Profit: There are two types; both are ratios with profit in the numerator. 1. Percent of profit based on cost is the ratio of profit to cost: 2. Percent of profit based on selling price is the ratio of profit to selling price: Obj 3: Profit and Percent of Profit (cont.)

27. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 5: Profit and Percent of Profit A retail store markets calculators that cost the store $45 each and are sold to customers for $60 each. a. What is the profit on each calculator? b. What is the percent of profit based on cost? c. What is the percent of profit based on selling price? Solution a. First find the profit. $60.00 –45.00 $1 00 Selling price Cost Profit

28. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 5: Profit and Percent of Profit (cont.) Solution For b. and c., use a ratio to find each percent of profit, and change the fraction to a percent. b. For percent of profit based on cost, remember that cost is in the denominator. c. For percent of profit based on selling price, remember that selling price is in the denominator. Profit based on cost Profit based on selling price

29. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 5: Profit and Percent of Profit A music store sells certain CD’s for $15 when the CD’s actually cost the store $6. a. What is the profit on each CD? b. What is the percent of profit based on cost? c. What is the percent of profit based on selling price? Solution a. First find the profit. $15.00 – 6.00 $9.00 Selling price Cost Profit

30. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 5: Profit and Percent of Profit (cont.) Solution For b. and c., use a ratio to find each percent of profit, and change the fraction to a percent. b.For percent of profit based on cost, remember that cost is in the denominator. c.For percent of profit based on selling price, remember that selling price is in the denominator. Profit based on costProfit based on selling price

31. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Obj 4: Tipping Tipping (or leaving a tip) is the custom of leaving a percent of a bill (usually at a restaurant) as a payment to the server for providing good service. Because you probably do not carry your calculator with you when dining out, the calculation of a 15% tip can be an interesting mental exercise in using percents.

32. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Obj 4: Tipping (cont.) The Short Method that we will use for finding a tip will use three basic facts: a. 10% of a decimal number can be found by moving the decimal point 1 place to the left b. 5% is one half of 10% c. 15% = 10% + 5%

33. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Short Method for Calculating a 15% Tip 1. For ease of calculation, round the amount of the bill to the nearest whole dollar. (Use the amount of the bill before the tax is added on.) 2. Find 10% of the rounded amount by moving the decimal point 1 place to the left. 3. Find 5% of the rounded amount by dividing the amount in Step 2 by 2. 4. Add the two amounts found in Step 2 and Step 3. This sum is the amount of the tip. Obj 4: Tipping (cont.)

34. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 6: Tipping You take your family out to dinner and the bill comes to $86.40 before tax. The tax is figured as 7.25% of the bill, and the total is $92.67. If you plan to leave a 15% tip, a. How much is the tip, and b. How much is the total bill?

35. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 6: Tipping (cont.) Solution a. For ease of computation, round $86.40 to $86.00. Find 10% of $86.00 by moving the decimal point 1 place to the left: Now find 5% of $86.00 by dividing $8.60 by 2: The amount of the tip is:

36. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 6: Tipping (cont.) Solution b. The total bill is: Note that we will give $105.57 as the official answer. However, practically speaking (depending on how much change you have in your pocket, how good the service was, or if you are paying by credit card) you might leave a tip of $10.00, $12.00, or $15.00, or leave a tip so that the total comes out even (such as $105.00). $92.67 + 1 90 $105.57 Amount of bill (tax included) Amount of tip Total bill

37. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 6: Tipping You and a group of friends go out to eat. Your bill comes to $17.20. The tax is figured at 5% of the bill and the total is $18.06. a. How much is the tip, and b. What is the total bill?

38. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 6: Tipping (cont.) Solution a. For ease of computation, round $17.20 to $17.00. Find 10% of $17.00 by moving the decimal point 1 place to the left: Now find 5% of $17.00 by dividing $1.70 by 2: The amount of the tip is:

39. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 6: Tipping (cont.) Solution b. The total bill is: $18.06 +2.55 $20.61 Amount of bill (tax included) Amount of tip Total bill