Ms. Campos -Math 7 Unit 8 Applying Percents

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1 Ms. Campos -Math 7 Unit 8 Applying Percents Date Lesson Topic Homework T 6 1/18 1 Introduction to Applications Lesson 1 Page 4 F 1 1/19 2 Deconstructing Percents Lesson 2 Page 7 M 2 1/22 3 Tax and Tip Lesson 3 Page 10 T 3 1/23 4 Commission Lesson 4 Page 13 W 4 1/24 Activity Finish Activity T 5 1/25 Quiz F 6 1/26 5 Discount Lesson 5 Page 15 M 1 1/29 6 Simple Interest Lesson 6 Page 20 T 2 1/30 Review Study! W 3 1/31 Activity Study! T 4 2/1 Test Name: # 1

Lesson 1: Introduction to Applications I can apply percentages to real world situations.

county and state in which the purchase is made.

Commission: The amount of money earned by a salesperson for selling a product; typically

Discount: An amount subtracted from the price of an item; a savings.

2 Lesson 1: Introduction to Applications I can apply percentages to real world situations. Unit Vocabulary Sales Tax: An amount of money added to a total purchase determined by the county and state in which the purchase is made. Tip: The amount of money earned by a person in the service industry for providing a particular service. Tips are usually given to waiters, valet, caddies, drivers and bellboys. Commission: The amount of money earned by a salesperson for selling a product; typically based on a percentage of the price of the product. Discount: An amount subtracted from the price of an item; a savings. Most percent word problems can be solved using the proportion: part whole % 100 This important proportion will be adjusted for each of the problem types that follow. ~Neat Fact~ "Percent" comes from the Latin Per Centum. The Latin word Centum means 100, for example a Century is 100 years. 2

3 Match the term to the example: 1) Uncle Johnny gave his waiter $20. 2) Elvis got an extra $45 in his paycheck from his sales this week. 3) Mike used a coupon and only spent $13 instead of $22. a) Sales Tax b) Tip c) Commission d) Discount 4) Even though I bought $10 worth of pencils, I had to pay $ ) Kent carried my bags up to my hotel room so I gave him $5. 6) Joyce bought a sequin top for 20% off. 7) Tommy made $340 plus his salary because he rented out a lot of apartments this week. 8) Porsche ordered three pairs of shoes for $20 each and was charged $ ) Phil only pays 50% because he is an employee. 10) Bill got to take home 20% of the value of his table s check. Find the following: 11) Kenny spent $6 out of $12. What percent of his money did he spend? 12) Todd had $44 in his wallet. He spent 30% of his money. How much money does he have left? 13) Peter spent 20% of his money. He has $40 left in his pocket. How much did he go out with? 3

4 Lesson 1: Introduction to Applications -- Homework Match the term to the example: 1) Sal only pays 80% of the bill because he counts the money. 2) Todd will bring your popcorn and drinks faster if you give him money. 3) Dave has to write a check to the State for the amount of money he collects over the subtotal. 4) Drew s boss gave him an extra $200 for having the highest sales. 5) Wendy will let you stay at the hotel for 20% less if you say sunshine when you book. 6) Justin makes 10% of the waiter s money because he bussed their tables and filled the ice. 7) The couple left Lynda a penny on a $300 bill because she was rude. 8) Casey paid for a $2 coffee at the store with a $5 bill and got back $2.84. a) Sales Tax b) Tip c) Commission d) Discount Solve for the missing number: 9) What is 42% of 87? 10) 22 is what percent of 88? 11) 17 is what percent of 51? 12) If each of the 58 people at Jay Leno show gives him $13 because he is doing a great job and his boss pays him $50 a show, how much money did Jay make at tonight s show all together? 13) Jackie kept $75 out of the $80 she found on the streets of NYC. What percentage did she keep? (Rounded to the nearest percent) 4

5 Lesson 2: Deconstructing Percents I can deconstruct percents to find the decimal or percent that will be paid. Warm Up: 1) Hahn had $25 left in her purse after shopping and spending 20% of her money. How much did she leave to go shopping with? 2) Ramon spent 60% of his $437 paycheck on gifts for his friends. How much did he spend? Deconstructing percents or decimals is finding the decimal or percent that you will actually pay for the item. When would you add the percent or decimal? Tax or Tip When would you subtract the percent or decimal? Sale or Discount Examples: 7% Tax = 1.07 or 107% Examples: 40% Sale = 60% or % Tip = 1.2 or 120% 15% Discount = 85% or 0.85 A. Guided Practice: Rewrite each as a final percent. 1. Tax of 12% 2. Discount of 12% 3. Tip of 18% 4. On sale for 18% off 5. 25% markup 6. 35% markdown 7. 20% gratuity 8. Pay a fine of 30% 9. 5% rebate % commission 11. An item depreciated 10% in value % coupon 5

6 B. Problem Set Determine if the following represent tax/tip or discount. State the percent change % % % % % % Write each decimal as a deconstructed percent x x 24. y 0.086y 25. a 0.2a 26. m

7 Lesson 2: Deconstructing Percents -- Homework Rewrite each percent as a final percent: A) If there was a tax/tip of that amount. B) If there was a discount of that amount. Ex. 22% A) 122% ( ) B) 78% (100 22) 1. 7% 2. 13% 3. 65% % Rewrite each percent as a final equivalent: A) Tax/Tip DECIMAL. B) Discount DECIMAL. Ex. 22% A) 1.22 ( ) B) 0.78 (1.0.22) 5. 7% 6. 13% 7. 65% % Solve the following using deconstructed percents or decimals: 9. You have lunch at Chili s and decide to leave a 20% tip, what is the final decimal that you will pay? 10. A Twilight DVD is 30% off the original price, what is the percent you pay for it? 7

8 Lesson 3: Tax and Tip I can apply proportional reasoning to calculate tax and tip. Warm Up: 1. If you pay 9% tax on a sweatshirt at Hollister, what is the decimal that you pay? 2. A coat is going on sale for 30% off, and you will have to pay 6% in tax, what is the final percent you will pay for the coat? How to find the Tax and Tip: Multiply cost by the percent as a decimal How to find the TOTAL PRICE or FINAL PRICE: Deconstructing percents! (%Tax/Tip + 100%) times Original $ Or Add the cost of the tax/tip to the original price A. Guided Practice 1) Liz buys a shirt that costs $25 and 8% sales tax. Find the tax. 2) Steve buys a polo shirt that costs $55 with a 6% sales tax. Find the total price. 3) The O Boyle s go to Chili s for dinner and spend $154 on their meal. They want to leave an 18% tip. Find the tip. 4) The boy s and girl s lacrosse teams went to the Hard Rock Café to celebrate the end of the season. They spent a total of $1040 and need to leave a 15% tip. Find the cost of the total bill. 8

9 5) Tom s bill at a restaurant was $ He plans to leave a 15% tip for the waiter. Explain how Tom can ESTIMATE the amount for the tip. 6) Mrs. DiJorio s math class all went out to lunch and spent a total of $600. There is a 5% tax and they want to leave a 15% tip. Find the final cost after tax and tip. 7) At a discount store, Cole offered a salesperson $600 for a couch. This offer includes the 8% sales tax. If the salesperson accepts the offer, what would be the price of the furniture, to the nearest dollar, before tax? B. Problem Set 1) Megan buys a pair of jeans for $40. There is an 8.5% sales tax. Find the tax. 2) Karl buys a mountain bike that costs $345 with a 9% sales tax. Find the total cost of the bike. 3) The Hochmuth s and their friends go to the Cheesecake Factory and spend $ They want to leave a 20% tip. Find the tip. 4) The 7 th grade class went to ESPN Zone and spent $4275. They want to leave an 18% tip. Find the total cost of the bill. 5) Mr. Webb goes on a jet skiing tour while on vacation. The company charges $199 and 6.25% in tax. After the tour, he gives the instructor a 15% tip on his debit card. How much did the whole excursion cost? 9

10 Lesson 3: Tax and Tip -- Homework **Reminder: Find the tip based on the original bill** 1) Patti works at a restaurant. She usually makes 15% tips on all the sales she makes for the night. If she had $784 in meals, estimate how much she could make in tips. 2) Terry wants to buy a Wii, but he is unsure if he has enough money. The Wii costs $300 and there is a 9% sales tax on it. If he has $325 does he have enough money? 3) Lowes charges $1.80 for a 10-foot board, plus 5% for preparation cost. a) If you need 50 boards, how much would the preparation cost be for all 50? b) What would the total cost be for all 50? 4) You and a friend go out for dinner and spend $ You want to leave a 15% tip. Your friend tells to leave $20. Is he right? Explain. How would you do this problem in your head? 5) A new phone costs $399.00, if tax is 7.5%, what is the total cost of the phone? 6) Bryce bought an aquarium priced at $ Shipping and handling cost him an additional 20%. What was the total cost of the aquarium, including shipping and handling? **7) Lynda was a horrible waitress. She spilled a drink on you and she brought you the wrong food. The bill came to $60 so you left her $3. What was the percent of tip you left her? 10

Lesson 4: Commission I can apply proportional reasoning to solve multistep commission problems. Warm Up: State the inequality. 1. 2. 3.

11 Lesson 4: Commission I can apply proportional reasoning to solve multistep commission problems. Warm Up: State the inequality Why do certain salespeople constantly try to convince you to buy something?? Remember: You can only find commission on the SALES. A salary is just added on to the commission at the end. A. Guided Practice 1) Kelly works at Game Stop. She earns an 8% commission for all sales. She sold $1500 in the month of November. a) What was her commission? b) If Kelly makes $300 per week base plus commission, how much did she earn in November? 2) Mr. Urbancik sells 12 CD s on ebay for $120. He gets a check for only $84 after the commission has been taken out. Find the commission percent charged by the site? 3) Kent is a real estate agent. He gets 2.5% commission on each house he sells. a) Find the commission Kent gets if he sells a house for $340,000. b) The day of the sale, Kent made a total of $10,000. How much of his salary did not include the commission from selling the house? 11

B. Problem Set 1) Eric gets a 7% commission for each electronics item he sells. If he sells $3000 worth of electronics, how much commission does he make?

If you sold two TVs for $60 each and a blow dryer for $12, how much commission do you make? How much money does your uncle walk away with? 3) A real estate agent sells condos for $90,000 each.

12 B. Problem Set 1) Eric gets a 7% commission for each electronics item he sells. If he sells $3000 worth of electronics, how much commission does he make? 2) Your Uncle is having a garage sale and asks you to come work it for him. You strike a deal for 3% of whatever you can sell. If you sold two TVs for $60 each and a blow dryer for $12, how much commission do you make? How much money does your uncle walk away with? 3) A real estate agent sells condos for $90,000 each. She earns a 4% commission. In May, she sold 9 condos. a) How much commission does she make on each condo? b) How much in commission did she receive in May? 4) Mandy s monthly earning consist of a fixed salary of $2800 and an 18% commission on all of her monthly sales. To cover her planned expenses, Mandy needs to earn an income of at least $6400 this month. a) Write an inequality, that when solved, will give the amount of sales Mandy needs to cover her planned expenses for the month. b) Graph the solution of the inequality on the number line below. 12

13 Lesson 4: Commission -- Homework 1) Dan is paid a 10% commission on his sales of $2300. He also made an additional bonus of 2% this month on those same sales. How much combined commission was earned? 2) Renee works in the shoe department at Saks 5 th Ave and has a salary that includes a base and a commission of 11% on all sales. If Renee makes $200 per week plus commission, how much does she make if she sold $6,500 worth of shoes? 3) Aaron, a car salesman at KIA, makes 4% commission on all sales. He sells 5 cars for $15,000 each. What was his total commission on his sales? **4) What is the commission percentage paid on a $450 diamond necklace if you make $50? Round to the nearest percent. 5) Will is a real estate agent. When he sells a house he gets 3% and if they buyers are his customers too, then he gets another 3%. How much money will he receive, if he sells the house for $345,000 to his customers? 6) Ken sells ovens at Lowes. He earns 5.6% commission on each oven sold. Today, he sold an oven for $1190. How much commission did he earn? 7) ebay charges a commission of 18% if the item sells for $500 or less. If the item sells for more than $500 it charges 18% for the first $500 and 9% on the amount over $500. a) Find the commission for a $400 sale b) Find the commission on a $650 sale 13

14 Lesson 5: Discount I can apply proportional reasoning to solve multistep discount problems. Warm Up: We the discount from the original amount. How to find the Discount: Multiply by the percent as a decimal How to find the SALES PRICE or FINAL PRICE: Deconstructing percents! (100% - Discount%) times Original $ OR Subtract the Discount from the Original Price A. Guided Practice 1) Scott buys a baseball bat for $45 but it is on sale for 25% off. Find the discount. 2) Carrie buys an outfit from Hollister for $75. If the discount is 15% off, find the sales price. 3) A coat is currently $ It is going on sale for 30% off. a) How much would you save? b) What will the new cost of the coat be? c) If 6% sales tax is now added, what is the final cost? 14

15 4) A comforter at Bed Bath & Beyond is $99 and you have a 20% off coupon. The same comforter is $99 at JC Penny s but is on sale for 15% off. You also have a coupon for 5% off your total purchase at JC Penny s. Which is the better deal? 5) You find sneakers for $79.95 at Modell s. In the paper, you see they will be on sale for $63.96 next week. a) What is the percent of discount that they will be offering? b) If you wait and buy them next week, you will also have a coupon for an additional 15% off your purchase. How much will the shoes cost you? B. Problem Set 1) Chris buys a dirt bike for $3050. The discount is 20% off. Find the discount. 2) Alex buys Rock Band for $150. The discount is 30% off. Find the sales price. 3) Ryan buys a 3-D HDTV for his brother while it was on sale for 15% off. The TV originally cost $2350. What is the sale price? 4) An XM radio player that lists for $398 in on sale for 30% off the list price. How much money do you save? 15

16 Lesson 5: Discount -- Homework 1) A laptop is on sale for 20% off the regular price. The price was originally $ What is the sale price? 2) A washing machine is on sale for 15% off of the list price of $620. a) What would the cost be after the savings? b) What would be the final cost of the machine after tax of 8.25% is applied? 3) This year the price of a gallon of gasoline dropped from $4.25 a gallon to $3.69 a gallon. Find the percent of discount to the nearest tenth? 4) A television on sale for 40% off saves you $184. What is the original price of the television? What is the sale price? 5) Last year there were 260 7th graders at Sagamore. This year the number of students decreased by 5%. How many less students are there? What is the new size of the 7th grade class? 16

17 Lesson 6: Simple Interest I can calculate simple interest by applying the formula, I=PRT. Warm Up: Change each percent to a decimal. 1) 25% 2) 33% 3) 4% 4) 134% 5) 2.5% Simple Interest: This is the amount of money you have to pay on a loan borrowed or you will earn in a bank. It is dependent on three factors: Principal, Rate and Time. I = PRT I = Interest is the amount of money you earn or pay. P = Principal is the money borrowed or invested. R = Rate is a percentage. You must change the percent to a decimal to solve the problem. T = Time is in years. If it is in months, you must convert it to years to solve the problem. Change each into years: A) 6 months B) 9 months C) 36 months D) 18 months A. Guided Practice. Calculate Simple Interest: 1) If you deposit $100 in a bank that pays 5% simple interest, how much interest will you earn in one year? 2) You borrow $500 at a simple interest rate of 4% for 6 years. How much interest will you owe? How much will you have to repay all together? 17

18 3) You borrow $500 at a simple interest rate for 6 years. If $240 is the interest earned, what was the rate for the interest? How much do you owe after 6 years? 4) You deposit $5000 at a simple interest rate of 2.5% for 6 months. How much interest is earned? 5) You get a student loan from the Bank of America to pay for your educational expenses each year. Find the interest on the loan if you borrowed $30,000 at 8% for 10 years. 6) You are starting your own small business. You borrow $10,000 from a bank at a simple interest rate for 5 years. If $650 is the interest earned, what was the rate of interest? B. Problem Set Calculate Simple Interest: 7) Some money was invested at 12% simple interest rate for 2 years. If the interest earned is $21, how much was invested? 8) Some money was invested for 3 years at 5% simple interest. If the interest paid was $60, how much money was invested? What was the total in the account after 3 years? 9) If you buy a car for $20,000 at an interest rate of 3% for 5 years, what is the simple interest? 18

19 10) You invest $1,500 for three years. Find the amount of simple interest you earn at an annual rate of 6.25%? 11) Suppose you invested $1,200 for four years. You earned $312 in simple interest. What is the interest rate? 12) If you buy a house for $525,000 at a simple interest rate of 7% for 15 years, how much are you actually paying for that house? 13) What is the interest if $4,500 is borrowed at 9.5% simple interest for 2 years 6 months? 14) $895 was invested for 2 years at 10% interest. How much total money do you have after the 2 years? 15) Explain whether you would earn more money from Plan A or Plan B. Plan A: $2, 500 for 7 years at 8%. Plan B: $2,500 for 8 years at 6% 19

20 Lesson 6: Simple Interest -- Homework 1) What is a reasonable ESTIMATE of the amount of money you will earn in interest on $620 invested at a 9% simple interest rate for 3 years? 2) Explain whether you would earn more money from Plan A or Plan B. Plan A: $1500 for 7 years at 8% Plan B: $1500 for 8 years at 7% 3) Scott agreed to pay back a loan in 4 months at a simple interest rate of 15% on $2500 he borrowed. What is the total amount he must re-pay? 4) What would you have to repay if you borrowed $700 at a simple interest rate for 4 years at 2%? 5) Mike borrows money from the bank to buy a new car. The loan is at a simple interest rate of 3% for 5 years. If the interest owed is $3000, how much was the loan originally for? 20

21 7R Unit 8 Review - Application of Percents Match the definition to the correct term: 1) A rate per 100 A) Discount 2) A percent of the amount of sales you make. B) Tip 3) Money added to the total purchase (depends of state and country). C) Commission 4) Money earned in a service industry. D) Percent 5) The amount subtracted from the price of an item. E) Percent of Change 6) The total amount after a discount. F) Sales Tax 7) The percent a quantity increases or decreases from the original amount. G) Sales Price 8) A local bakery sold 60 loaves of bread in one day. If 65% of these were sold in the afternoon, how many loaves were sold in the afternoon? 9) 24 is what percent of 120? 10) 3 is 12% of what number? 11) Anna has 220 coins in her piggy bank. Of those, 45% are pennies. How many coins are NOT pennies? 12) The price of a new version of a computer game is 120% of the price of the original version. The original version cost $48. What is the cost of the new version? Remember that you have TWO options for finding the tax and tip. Option 1: Use a percent proportion Option 2: Take the full 100% plus the percent of tax or tip. 13) A customer wants to tip 15% on a restaurant bill that is $35. What will be the total bill with tip? 14) Drew wants to buy exercise equipment that costs $140 and the sales tax is 5.75%. What is the total cost of equipment? 21

22 15) Find the total cost of a spa treatment of $54 including 6% tax and 20% tip. 16) A haircut costs $20. Sales tax is 4.75%. Is $25 sufficient to cover the haircut with tax and a 15% tip? 17) Ryan wants to tip his taxicab driver 20%. If his commute costs $15, what is the total cost? Commission 18) Find the commission on a diamond that is sold for $6700 when the commission paid is 4%. 19) Find the commission of a $700 sale with 9% commission rate. 20) Jay works at PC Richard s and makes a weekly salary of $400. In one week he sold $1500 worth of electronics. If he makes a 3% commission on all sales, how much money did Jay bring home that week? 21) Mrs. O Boyle works at the local Jewelry store on the weekends. In one weekend, she sold $3600 worth of merchandise and made $216 in commission. What was the rate of commission? Discount 22) A DVD normally costs $22. This week it is on sale for 25% off the original price. What is the sale price of the DVD? 23) A shirt is regularly priced at $42. It is on sale for 15% off of the regular price. How much will you save with the discount? 22

23 24) A bottle of lotion is on sale for $2.25. If this price represents a 50% discount from the original price, what is the original price to the nearest cent? 25) A boogie board that has a regular price of $70 is on sale at a 35% discount. What is the sale price with 7% tax? 26) Find the sales price of a $64 jacket with a 20% discount. 27) Find the percent discount of a shirt that originally costs $60 and was reduced to $39. Simple Interest 28) Find the simple interest if $4500 was invested at 6% simple interest rate for 4 years. 29) Find the amount borrowed at a 3% interest rate for 2 years, if $30 was earned in interest. 30) If $6000 was borrowed at a simple interest rate of 3.5% for 5 years, how much is owed with interest included? Mixed Review 31) -4 (-100) 32) )

24 34) The highest official recorded temperature for Chicago is 107 F in The lowest official recorded temperature is 27 F in What is the difference between these temperatures? 35) 7x + 5 = 40 36) -2(4 x) = ) 1 (2x 8) ) The scale on a drawing is 0.5in : 15ft. Find the actual length for a drawing that is 20inches. 41) Solve the following proportion: 42) Find the unit rate: x calories in 5 crackers 43) Find the constant of proportionality: Hours (h) Songs

Lesson Understanding Percents Working with Mental Percents 3 Cases of Percents Percent Change Quiz Deconstructing Percents Percent Error Extra Day

Lesson Understanding Percents Working with Mental Percents 3 Cases of Percents Percent Change Quiz Deconstructing Percents Percent Error Extra Day Unit 7 Percent Lesson 1 Understanding Percents 2 Working with Mental Percents 3 3 Cases of Percents 4 Percent Change Quiz 5 Deconstructing Percents 6 Percent Error Extra Day Review Test 1 Vocabulary Lesson