Learning Target: I can… Use a proportion to find percent increase and decrease

Percent Increase and Decrease Percent Increase: when the value exceeds 100% of the original value Percent Decrease: when the value is less than 100% of the original value

To Find a New Value 1) Use a ____________________ to solve percent increase and decrease problems. 2) The increase or decrease gets ________ or ________ to/from 100. In the proportion, this number goes over _________. 3) The original value should match up with 100.

Example 1 The Waynesville High School library has 500 books. Next year, they would like to increase the number of books they have by 52%. If they reach their goal, how many books would they have next year?

Example 2 The Waynesville High School band has 45 members Example 2 The Waynesville High School band has 45 members. Next year, they would like to increase their membership by 20%. If they reach their goal, how many members would they have next year?

Example 3 The Dayton Transportation Department recorded 200 crashes in October. Next month, they would like to decrease their crashes by 25%. If they reach their goal, how many crashes would they have next month?

Example 4 The Dayton Fire Department recorded 120 fires in October Example 4 The Dayton Fire Department recorded 120 fires in October. Next month, they would like to decrease the fires by 20%. If they reach their goal, how many fires would they have next month?

To find a percent increase or decrease: Example 1: Janie starts playing sports and gets into shape. She goes from 125 pounds to 110 pounds. Is this a percent increase or decrease? What was her percentage weight loss? *Remember: the original value always matches up with 100

2) Growing up, you lived in a tiny country village. When you left for college, the population was 840. You recently heard that the population was 882. Is this a percent increase or decrease? What is the percent change?

3) One week 24 people in Waynesville got speeding tickets. The next week only 16 people got speeding tickets. Is this a percent increase or decrease? What is the percent change?

4) Last year, only 8 athletes played on the girls tennis team. This year 10 people played. Is this a percent increase or decrease? By what percentage?

Mix it up

A girl was 4 ft 9 in. tall last year. This year she is 5 ft tall A girl was 4 ft 9 in. tall last year. This year she is 5 ft tall. Find the percent of increase in her height. Round to the nearest tenth of a percent. 2.0% 5.3% 5.0% 153.0%

When the first US Census was taken in 1790, the population was 3,929,200. In the most recent census, the population was 308,745,538. What is the percent increase rounded to the nearest tenth?

Last year 300 kids went to Waynesville Middle School Last year 300 kids went to Waynesville Middle School. This year, 350 kids go to Waynesville Middle School. What is the percent of change?

In the 1986 Olympic Games, Ellery Clark of the US jumped 20 ft 10 in to win the men’s long jump. In a recent Olympics, an athete jumped 28 ft 0.75 inches to win the men’s long jump. Find the percent of increase or decrease in the length of the men’s winning long jump.

OAA Practice: What has the greatest percent of change? A tree grew from 6 feet to 12 feet An aquarium that was originally priced at $80 is now $60 A person whose salary was $100 per week is now earning $120 per week A baby who weighed 7 pounds at birth now weighs 16 pounds

EXIT

Learning Target: I can… Calculate tax, gratuity and total bill

Percent Vocabulary Gratuity: Wholesale price: Retail Price: Markup: Markdown: Commission: Interest:

Vocabulary Gratuity: (Tip) A percent earned by a person for providing a service

Tax The tip is a ___________________ of your bill Step 1: ____________________ the percent by the bill to get the tip Step 2: ___________ the answer to ____________________________

Tips You want to leave a 15% tip. If your meal costs $10, how much should you leave for a tip? How much did you spend altogether? Step 1: Multiply (to get your tip) Step 2: Add tip to the original amount to get the total!

Example 2: You want to leave a 20% tip Example 2: You want to leave a 20% tip. If your meal costs $15, how much should you leave for a tip? How much did you spend altogether?

Example 3: If they only ask for your final payment: You want to leave a 15% tip. If your meal cost $30, how much did you spend altogether?

Tips Example 4: Your bill at Bob Evans is $25.00. If you want to leave 20% gratuity, what will be the total amount that you spent? $25.00

Your parents took your family out to dinner Your parents took your family out to dinner. Your parents wanted to give the waiter a 15% tip. If the total amount of the dinner was $42, how much should be paid to the waiter as a tip? How much will you spend all together?

Going Backwards: Example 1 Justin leaves a tip of $6, which was 20% of the cost of his meal. How much did his meal cost?

Example 2 Eric’s family leaves a tip of $18, which was 15% of the cost of their bill. How much did their meal cost?

Vocab: Sales Tax: A percent of a purchase charged by the government Tax is a ___________________ OF your purchase Step1: ____________________ the percent by the purchase to get the tax Step 2: ___________ the answer to ____________________________

Sales Tax The sales tax is 6.5%. If you buy a television for $500, what will your total price be? Step 1: Multiply the percent by your price (to get your tax) 6.5% x 500 = 32.5 or 32.50 Step 2: Add tax to the original amount to get the total! 500 + 32.50 = $532.50 Total Price

You try it! The sales tax is 7%. If you spent $60 on items, how much is your sales tax? $4.20 Including tax, how much did you spend? $64.20

Example 3 Menu: Hamburger meal $8.75 Drink $2.50 You and your friend each order a hamburger meal and a drink. What is your total amount you will spend? What is the tax of the meal with a 6.5% tax? What is the final bill?

Example 4 Example 4: The bill for a family dinner was $49.53. What is the bill with a 6.5% tax? What is the total so far? Mr. Jones wants to leave about 15% of the bill as a tip. What is the tip?   What is the total amount he paid?

Exit Find total amount spent at Best Buy if you bought a $200 TV and paid 7% tax. 2. Find the total amount spent at a restaurant if the bill is $30 and you tip 20%.

Learning Target: I can… Calculate markdowns

Markdown: (Discount): A percent or amount of decrease in the price of an item Wholesale price: The price a retail store pays the manufacturer Markup: A percent or amount increase a retail store charges to earn a profit Retail price: The price at which a store sells items to customers (wholesale price + markup)

To calculate discounts and/or multiple discounts: Step1: ____________________ the percent by the purchase Step 2: ___________ the answer from ____________________________ (Sometimes) Step 3: _____________ the additional percentage by the new sale price (Sometimes) Step 4: _____________ the additional discount by the new sale price

1. Find 30% off of a CD that cost $15.

2. A stereo is $56. 80. It is marked as 15% off the original price 2. A stereo is $56.80. It is marked as 15% off the original price. What is sale price?

3. A sweater is selling at a discount of 45%. The original price is 49 3. A sweater is selling at a discount of 45%. The original price is 49.60. What was the sale price of the sweater?

The sweater shack is offering a 20% discount on sweaters The sweater shack is offering a 20% discount on sweaters. If the regular price of the sweater is $15.00, what is the discount? Subtract the discount you found from the original price to find the sale price.

Jean Junction is selling jeans at 25% off Jean Junction is selling jeans at 25% off. The regular price of the jeans are $40. What is the discount? What is the sale price?

A video game store has a 20% discount on all video games A video game store has a 20% discount on all video games. The video game you want is $32. What is the discount? What is the sale price?

Dacor Appliances is selling its $450 washing machine for 15% off the regular price. What is the discount? What is the sale price?

You try it! The original price of a DVD is $20.00. If it is discounted 15%, what is the new price of the DVD? 17

Elise is buying two coats for her children. Margaret’s coat costs $40 Elise is buying two coats for her children. Margaret’s coat costs $40.00 but is 25% off. Justin’s coat cost $34.00 but is 10% off. Which coat is the better deal? If she buys them both, how much will she spend? (without tax)

Discounts and Tax 1) A pair of jeans that you want to buy costs $24.00. The jeans are on sale for 15% off. Sales tax is 7% added to the price. What will the total be at the checkout? What is the discounted price? _________ What is 7% of the discounted price _______ What is your final total at checkout ________

2) Aimee is decorating her new house 2) Aimee is decorating her new house. She found a table at Pier One for $425. If the table is 25% off and she has to pay a 6% tax, what will be her final price at checkout? What is the discounted price? ________ What is 6% of the discounted price? ______ What is your final total at checkout? ___________

Multiple Discounts 1)

2)

3) Extended Response Example

Going Backwards (to find the original price) It may be helpful to set up a ___________________________. Example 1: A TV is selling at a discount of 25%. The sale price is $609.75. What was the original price of the TV?

Example 2: A shirt is selling at a discount of 10%. The sale price is $27.00. What was the original price of the TV?

EXIT The new price of a pair of pants is $30.00. find the original price if the pants are discounted 20%.

EXIT The original price of a pair of pants is $30.00. find the new price if the pants are discounted 20%.

Learning Target: I can… Solve multi-step word problems involving percent

Review – Gratuity Step 1: __________________ the percent by the bill to get your tip. Step 2: _____________ your answer to the original bill

Review – Gratuity 1. Janet got lunch at Deb’s Diner. She spent $2.25 on a drink, $7.99 on a sandwich, and $3.76 on dessert. She also left a 20% tip. How much did she spend altogether?

Markdown Step 1: __________________ the percent by the purchase to get the discount Step 2: _____________ your answer from the original bill

Review - Discount The sweater shack is offering a 15% discount on sweaters. If the regular price of the sweater is $18.00, what is the new price of the sweater?

Multiple Discounts Step 1: _____________ the percent by the cost Step 2: _____________ the discount from the cost Step 3: _____________ the addition percentage by the new cost Step 4: _____________ the discount from the cost

1) Stacy went to the shopping mall 1) Stacy went to the shopping mall. While she was shopping, she found a coat she liked that was on sale. The coat originally cost $120 but had been reduced by 35%. The store was having a red tag sale that day, so she got an addition 10% off the sale price. How much did Stacy pay for the coat? $42.50 $66.00 $70.20 $78.00

2) The original price of a GPS system was $105 2) The original price of a GPS system was $105. It was on sale at a 20% discount. Later, the price of the GPS was reduced by an additional 10%. What was the final price of the system?

Tax and Discount Step 1: _______________ the percent by the purchase to get the discount. Step 2: ____________ your answer from the original bill Step 3: _____________ the percent tax by the new bill to get the tax Step 4: __________ the tax to your bill

Tax and Discounts Andrea works as a cashier in a music store. A customer wants to pay for a CD that is on sale for 15% off the regular price of $14.00. Andrea needs to add 7% sales tax to the sale price of the CD. What should Andrea charge the customer for the CD, including tax?

Clicker Check A pair of jeans that you want to buy costs $40.00. The jeans are on sale for 20% off. Sales tax is 7% added to the price. What will the total be at the checkout?

Working Backwards A TV is selling at a discount of 20%. The sale price is $799.20. What was the original price of the TV?

The price of purchase was $53 after tax The price of purchase was $53 after tax. If the tax was 6%, what was the cost before tax.

EXIT Ronny wants a pair of jeans that cost $40. The jeans are on a markdown rack of 20% off. Ronny has a coupon that says “take an additional 10% off clearance items.” What is the final cost of the jeans (without tax)?

RED, YELLOW, GREEN 6 – 7 correct, GET THE RED PAPER 3 – 5 correct, GET THE YELLOW PAPER 0 – 2 correct, GET THE GREEN PAPER

GREEN Name__________________________ *ALL OGT Questions* 1) 2) 3) Kelsey bought flowers from a florist for her mom’s birthday. Kelsey bought a dozen roses and was charged $20.25. If tax was 6%, how much did each rose cost before tax?

4) A local art museum charges admission to groups according to the following rates. Groups of fewer than 50 people are charged a rate of $4.00/person. Groups of 50 people or more are charged a reduced rate of 12.5% off per person. How much money will a group of 49 people save in admission costs if it can recruit one additional member? 5) 6)

YELLOW Name__________________________ OGT Question 1) OAA Question 2) COUPON 1 pair of shorts regular priced ______ +1 pair half off ______ Equals ______ SALE 30% off the first pair of shorts _____ +30% off the second pair ______ Equals _______ Conclusion: OAA Question 30% with addition 10% 30% discount ______ Subtract to find sale price ______ 10% of THAT SALE PRICE ______ Subtract to find final price _______ 40% 40% discount _____ Subtract to find sale price______ Conclusion (are the answers the same, or how are they different?): 2) During a sale, the price of all televisions in a store is being reduced by 30%. Sam is interested in a television with an original cost of $650. Two weeks later, the same price of this television is reduced by an additional 10%. Sam thinks he can now get the television for 40% off the original price. Describe how the same price with an additional 10% reduction is different than a single reduction of 40%. Use mathematics to justify your answer.

3) Joe wants to buy a shirt that is regularly $20 3) Joe wants to buy a shirt that is regularly $20.00, but today it is on sale for 40% off. When he gets to the register, he remembers that he will have to pay 6.5% sales tax on the shirt as well. What is his total? DISCOUNT Take 40% of 20 ______ Subtract this answer from 20 ______ TAX Take your FINAL ANSWER from discount and multiply it by 6.5%_____ Add this answer to your FINAL ANSWER from discount______ FINAL ANSWER: 4) *no hints*

RED Name__________________________ *Questions with hints* 2) 1) Jean Junction is selling jeans at 25% off. The regular price of the jeans are $40. What is the discount? TO SOLVE: Multiply 25% by 40 What is the sale price? TO SOLVE: Subtract 35 by the discount that you just calculated A shirt costs $35. There is a 16% discount. What is the discount? TO SOLVE: Multiply 16% by 35 How much do you pay for the shirt? TO SOLVE: Subtract 35 by the discount that you just calculated *Questions without hints* 3) The sweater shack is offering a 20% discount on sweaters. If the regular price of the sweater is $15.00, what is the discount? What is the new price? 4) A video game store has a 20% discount on all video games. The video game you want is $32. What is the discount? What is the sale price? *OAA Questions with hints* *OAA Question without hints* 5) 6) Step 1: Take 25% of 40 ______ Step 2: Subtract your answer from 40 ______ Step 3: Take 10% of step 2’s answer ______ Step 4: Subtract step 3’s answer from the step 2’s answer ______

Step 2: Subtract your answer from 50 ______ You Try! Daniel bought a pair of pants that were on sale for 30% off, plus an additional 10% off the marked down price. The original price of the pants was $50. What was the final price of the pants? Step 1: Take 30% of 50 ______ Step 2: Subtract your answer from 50 ______ Step 3: Take 10% of step 2’s answer ______ Step 4: Subtract step 3’s answer from the step 2’s answer ______ July 5: Take 20% of 3,900 _____ Subtract your answer from 3,900 ______ July 6: Take 20% of July 5’s answer ______ Subtract this from July 5’s answer _______ Continue until your answer is under $2,200

CPS Mini Quiz Name__________________________ 2. Janet got lunch at Deb’s Diner. She spent $2.25 on a drink, $7.99 on a sandwich, and $3.76 on dessert. She also left a 20% tip. How much did she spend altogether? 1. The sweater shack is offering a 15% discount on sweaters. If the regular price of the sweater is $18.00, what is the new price of the sweater? 3. The original price of a GPS system was $105. It was on sale at a 20% discount. Later, the price of the GPS was reduced by an additional 10%. What was the final price of the system? 4. A pair of jeans that you want to buy costs $40.00. The jeans are on sale for 20% off. Sales tax is 7% added to the price. What will the total be at the checkout? 5. A TV is selling at a discount of 20%. The sale price is $799.20. What was the original price of the TV?

Learning Target: I can… Solve real-life word problems involving percent

Exit You are buying 2 sets of pajamas. Which store has the better buy and how much would you spend? Babies R Us Buy 1 pair and get one half off. Original price: $20.00 Target Each pair is 30% off. Original price: $20.00

Learning Target: I can… Find the better buy

EXIT Sarah’s Shoes is having a deal where you can buy one pair of shoes and get another half off. The shoes cost $40 per pair. Steve’s Sneakers has a special where you can get 20% off each pair you buy. The shoes originally cost $35 per pair. If you want to buy 2 pairs, which store has the better deal and how much will you spend?

Learning Target: I can… Solve word problems involving interest

Simple Interest A percentage of a principal amount Formula: I = P x R x T Where I is ___________________ P is _________________ or ____________ R is ___________ T is ___________

1) Suppose a bank is offering its customers 3% interest on savings accounts. If a customer deposits $1500 in the account, how much interest does the customer earn in 5 years? How much does the customer have in the bank after 5 years?

2) Kelly plans to put her graduation money into an account and leave it there for 4 years while she goes to college. She receives $750 in graduation money that she puts it into an account that earns 4.25% interest. After 4 years, how much has Kelly earned in interest? How much will be in Kelly’s account at the end of four years?

3) Suppose you put $200 in an account that pays simple interest 3) Suppose you put $200 in an account that pays simple interest. The bank will pay you 5% interest annually. How much interest will you earn in three years? How much total will you have in your account after three years?

4) Adam plans to put his birthday money into an account and leave it there for 10 years. He receives $400 in birthday money that he puts into an account that earns 5% interest. After 10 years, how much has Adam earned in interest? How much will be in Adam’s account at the end of ten years?

Working Backwards I = $200 P = $1000 t = 5 years Find the interest rate.

Working Backwards I = $9 P = $200 t = 18 months Find the interest rate.

You put $300 in a savings account You put $300 in a savings account. The account earns $6 simple interest in 6 months. What is the annual interest rate?

Finding the time Find the amount of time I = $30, P = $500, r = 2%

Finding the time Find the amount of time I = $144, P = $600, r = 4%

Vocab Commission: A percent of total sales earned by an employee or business

Donald is a car salesman Donald is a car salesman. Donald makes 10% commission on every car he sells. If he sells a car for $30,000, how much money does Donald make?

Leo is a sells suits. He earns 30% commission for each suit he sells Leo is a sells suits. He earns 30% commission for each suit he sells. If he sells 5 suits and they each cost $200, how much did he earn in commission?

Tara is a sales representative for a cosmetic company. She is paid $5 Tara is a sales representative for a cosmetic company. She is paid $5.15 per hour each week plus a commission of 10% of the amount of sales over $5000. She works 40 hours one week, and she sells $7260 worth of cosmetics during that week. How much commission does she make? How much money does she make total?

Ryan is a sales representative for an insurance company Ryan is a sales representative for an insurance company. He is paid $10 per hour each week plus a commission of 5% of the amount of sales (of insurance plans) over $2,000. He works 40 hours one week, and he sells $5,000 worth of insurance during that week. How much commission does she make? How much money does he make total that week?

Exit Find the interest if Ayanna invested $5000 for 5 years at a rate of 3.5%. How much does she have in the bank now? Homework – page 140

Learning Target: I can… Solve word problems involving markup

Wholesale price: The price a retail store pays the manufacturer Markup: A percent or amount increase a retail store charges to earn a profit Retail price: The price at which a store sells items to customers (wholesale price + markup)

To Find the Retail Price: Step 1: ______________ the wholesale price by the markup rate Step 2: ____________ the answer to the wholesale price to get the retail price

1) A computer software retailer used a markup rate of 40% 1) A computer software retailer used a markup rate of 40%. Find the selling price of a computer game that cost the retailer $25.

2) A store that sells skateboards buys them from a manufacturer at a wholesale price of $57. The store’s markup is 150%. What is the retail price?

3) A store buys guitars from a manufacturer at a wholesale price of $38. The store’s markup is 85%. What is the retail price?

4)

Critical Thinking A $140 car stereo is marked up 50% and then discounted 50%. Will the final price of the car stereo be $140? Explain.

To find the wholesale price Use a proportion: Step 1: __________________ the markup percentage to 100% Step 2: Put the new percentage over _________________ Step 3: Always match up the wholesale price (x) with 100

1) A shoe store uses a 40% markup on cost 1) A shoe store uses a 40% markup on cost. Find the wholesale price of a pair of shoes that sells for $63.

Find the wholesale price 2) A bathing suit store uses an 80% markup on cost. Find the wholesale price of a bathing suit that sells for $40.

Find the rate of markup To Find the Markup Rate Step 1: Write a ratio of retail to wholesale Step 2: Put the percentage (x) over____________ Step 3: Always match up the wholesale price (x) with _______________ Step 4: _______________________the answer from 100

Find the rate of markup 1) A golf shop pays its wholesaler $40 for a certain club, and then sells it to a golfer for $75. What is the markup rate?

Find the rate of markup 2) A tennis shop pays its wholesaler $20 for a certain racket, and then sells it to a tennis player for $50. What is the markup rate?

Profit 3) A store buys an item for $20. To earn a profit of $30, what percent does the store need to markup the item?

Profit 4) A store buys an item for $10. To earn a profit of $20, what percent does the store need to markup the item?

EXIT Target buys a box of cereal for $1.50. If they mark up the cereal 80%, what price do they sell if for?

Homework – Page 136 in Record and Practice Journal

Percent Error

Learning Target: I can… Review for my ratio, proportion and percent test

Vocab Commission: A percent of total sales earned by an employee or business

Donald is a car salesman Donald is a car salesman. Donald makes 10% commission on every car he sells. If he sells a car for $30,000, how much money does Donald make?

Leo is a sells suits. He earns 30% commission for each suit he sells Leo is a sells suits. He earns 30% commission for each suit he sells. If he sells 5 suits and they each cost $200, how much did he earn in commission?

Tara is a sales representative for a cosmetic company. She is paid $5 Tara is a sales representative for a cosmetic company. She is paid $5.15 per hour each week plus a commission of 10% of the amount of sales over $5000. She works 40 hours one week, and she sells $7260 worth of cosmetics during that week. How much commission does she make? How much money does she make total?

Ryan is a sales representative for an insurance company Ryan is a sales representative for an insurance company. He is paid $10 per hour each week plus a commission of 5% of the amount of sales (of insurance plans) over $2,000. He works 40 hours one week, and he sells $5,000 worth of insurance during that week. How much commission does she make? How much money does he make total that week?

EXIT Proportion Review: Matty was boiling a pot of water on the stove. The temperature rose from 52°F to 92°F in 30 seconds. How many minutes would it take for the temperature to boil (rise from 52°F to 212°F)?

Learning Target: I can… Show what I know on my ratio, proportion and percent test

EXIT Suppose that a ladybug can fly 70 feet in 5 seconds. A bee can fly 102 feet in 6 seconds. Which can fly faster and by how much?

Learning Target: I can… Explain my misconceptions and correct my mistakes

EXIT Carla rides her bike 2 miles to school each day. She leaves her house at 7:00 and arrives at 7:20. What is Carla’s average speed in miles per hour?

Learning Target: I can… Write expressions involving percents

Writing Expressions Discount If p is the original price of an item, write the expression for a 20% discount. p – .2p or 0.8p Example 2: Discount If p is the original price of an item, write the expression for a 15% discount.

Tax If p is the original price of an item, write the expression for a total purchase of an item with 3% tax. p + .03p or 1.03p Tax Example 2: If p is the original price of an item, write the expression for a 15% discount.

Tax and Discount If p is the original price of an item, write the expression for a total purchase of an item with a 20% discount and a 3% tax. 0.8p + 0.03(0.8p) 1.03p – 0.20(1.03p)