This document provides definitions and formulas for key concepts in social arithmetic including selling price, markups, markdowns, discounts, commissions, sales tax, profit, and simple interest. It includes examples of how to calculate these values using basic formulas involving cost, selling price, rate, principal, time and other variables. Calculations include determining dollar amounts, percentages, and total values for problems involving retail prices, loans, investments and other financial transactions.

1. Social Arithmetic Selling Price, Mark-ups Markdowns, Discount, Commission, Sales Tax, Profit & Simple Interest TOPIC 9

2. Terminology Selling Price - The price retailers charge customers Cost - The price retailers pay to a manufacturer Markup, margin, or gross profit - The difference between the cost of bringing the goods into the store and the selling price Operating expenses or overhead - The regular expenses of doing business such as rent, wages, utilities, etc. Net profit or net income - The profit remaining after subtracting the cost of bringing the goods into the store and the operating expenses

3. Basic Selling Price Formula Selling price (S) = Cost (C) + Markup (M) $1,200 Computer $900 - Price paid to bring computer into store $300 - Dollars to cover expenses and profit

7. Markdowns Carrefour marked down a $50 tool set to $36. What are the dollar markdown and the markdown percent? $36 $14 $50 28% $50-$36 Markdown Markdown percent = Dollar markdown Selling price (original)

8. DISCOUNT

9. Discount is the difference between the regular price and the sale price of an item. You can use percent of decrease to find discounts.

10. Sarah bought a DVD player originally priced at $450 that was on sale for 20% off. What was the discounted price? Example 1: Finding Discount (450)(0.20) = 90 Find 20% of $450. This is the amount of discount. 450 – 90 = 360 Subtract $90 from $450. Multiply, then subtract. The discounted price was $360.

11. Example 2: Finding Discount (85)(0.40) = 34 Find 40% of $85. This is the amount of markup. 85 + 34 = 119 Add $34 to $85. Multiply, then add. Mr. Olsen has a computer business in which he sells everything 40% above the wholesale price. If he purchased a printer for $85 wholesale, what will be the retail price? The retail price is $119.

12. Check It Out! Example 3A (750)(0.10)= 75 Find 10% of $750. This is the amount of discount. 750 – 75 = 675 Subtract $75 from $750. Multiply, then subtract. Lily bought a dog house originally priced at $750 that was on sale for 10% off. What was the sale price? The sale price was $675.

13. COMMISSION

14. A commission is a fee paid to a person who makes a sale. It is usually a percent of the selling price. This percent is called the commission rate . commission rate  sales = commission Commission

15. A real-estate agent is paid a monthly salary of $900 plus commission. Last month he sold one condominium for $65,000, earning a 4% commission on the sale. How much was his commission? What was his total pay last month? Multiplying by Percents to Find Commission Amounts First find his commission. 4%  $65,000 = c commission rate  sales = commission 0.04  65,000 = c Change the percent to a decimal. 2600 = c Solve for c.

16. Example 1 Continued He earned a commission of $2600 on the sale. Now find his total pay for last month. $2600 + $900 = $3500 commission + salary = total pay. His total pay for last month was $3500. A real-estate agent is paid a monthly salary of $900 plus commission. Last month he sold one condominium for $65,000, earning a 4% commission on the sale. How much was his commission? What was his total pay last month?

17. A car sales agent is paid a monthly salary of $700 plus commission. Last month she sold one sports car for $50,000, earning a 5% commission on the sale. How much was her commission? What was her total pay last month? Check It Out! Example 1 First find her commission. 5%  $50,000 = c commission rate  sales = commission 0.05  50,000 = c Change the percent to a decimal. 2500 = c Solve for c.

18. Check It Out! Example 1 Continued The agent earned a commission of $2500 on the sale. Now find her total pay for last month. $2500 + $700 = $3200 commission + salary = total pay. Her total pay for last month was $3200. A car sales agent is paid a monthly salary of $700 plus commission. Last month she sold one sports car for $50,000, earning a 5% commission on the sale. How much was her commission? What was her total pay last month?

19. SALES TAX

20. Sales tax is the tax on the sale of an item or service. It is a percent of the purchase price and is collected by the seller. Sales Tax

21. If the sales tax rate is 6.75%, how much tax would Adrian pay if he bought two CDs at $16.99 each and one DVD for $36.29? Example : Multiplying by Percents to Find Sales Tax Amounts $70.27 Total Price 0.0675  70.27 = 4.743225 Write the tax rate as a decimal and multiply by the total price. Adrian would pay $4.74 in sales tax. CD: 2 at $16.99 $33.98 DVD: 1 at $36.29 $36.29

22. Check It Out! Example 2 Amy reserves a hotel room for $45 per night. She stays for two nights and pays a sales tax of 13%. How much tax did she pay? $45  2 = $90 Find the total price for the hotel stay. $90  0.13 = $11.70 Write the tax rate as a decimal and multiply by the total price. Amy spent $11.70 on sales tax.

23. Profit

24. A furniture store earns 30% profit on all sales. If total sales are $2790, what is the profit? Example 3A: Finding Profit and Total Sales Think: What is 30% of 2790? x = 0.30  2790 Set up an equation. x = 837 The profit is $837. Multiply.

25. Think: 10,044 is 30% of what number? Let s = total sales 10,044 = 0.30  s Set up an equation. 33,480 = s Simplify. The total sales are $33,480. A furniture store earns 30% profit on all sales. If the store earns $10,044, how much are the total sales? Example 3B: Finding Profit and Total Sales 10,044 0.30 = Divide each side by 0.30. 0.30 s 0.30

26. A retail store earns 40% profit on all sales. If total sales are $3320, what is the profit? Check It Out! Example 4A Think: What is 40% of 3320? x = 0.40  3320 Set up an equation. x = 1328 The profit is $1328. Multiply.

27. Think: 5,680 is 40% of what number? Let s = total sales 5,680 = 0.40  s Set up an equation. 14,200 = s Simplify. The total sales are $14,200. A furniture store earns 40% profit on all sales. If the store earns $5,680, how much are the total sales? Check It Out! Example 4B 5,680 0.40 = Divide each side by 0.04. 0.40 s 0.40

28. SIMPLE INTEREST

29. When you deposit money into a bank, the bank pays you interest. When you borrow money from a bank, you pay interest to the bank. I = P  r  t Simple interest is money paid only on the principal. Principal is the amount of money borrowed or invested. Rate of interest is the percent charged or earned. Time that the money is borrowed or invested (in years).

40. Mr. Johnson borrowed $8000 for 4 years to make home improvements. If he repaid a total of $10,320, at what interest rate did he borrow the money? Additional Example 4: Finding the Rate of Interest P + I = A Use the formula. 8000 + I = 10,320 Substitute. I = 10,320 – 8000 = 2320 Subtract 8000 from both sides. He paid $2320 in interest. Use the amount of interest to find the interest rate.

41. Additional Example 4 Continued 2320 = 32,000  r Simplify. I = P  r  t Use the formula. 2320 = 8000  r  4 Substitute. 0.0725 = r 2320 32,000 = r Divide both sides by 32,000. Mr. Johnson borrowed the money at an annual rate of 7.25%, or 7 %. 1 4

42. Mr. Mogi borrowed $9000 for 10 years to make home improvements. If he repaid a total of $20,000 at what interest rate did he borrow the money? Check It Out! Example 4 P + I = A Use the formula. 9000 + I = 20,000 Substitute. I = 20,000 – 9000 = 11,000 Subtract 9000 from both sides. He paid $11,000 in interest. Use the amount of interest to find the interest rate.

43. Check It Out! Example 4 Continued 11,000 = 90,000  r Simplify. I = P  r  t Use the formula. 11,000 = 9000  r  10 Substitute. Mr. Mogi borrowed the money at an annual rate of about 12.2%. 11,000 90,000 = r Divide both sides by 90,000. 0.12 = r