Unit 8Applying Percents

Lesson Topic Standard1 Introduction to applications (vocabulary)

Commission, discount, tip, (real world)7 RP3

2 Tax/tip (tax + tip) 7 RP33 Commission 7 RP34 Discount (discount + tax) 7 RP35 Simple Interest6 Review Sheet7 Test

Name: _______________Teacher: ____________

Period: __________

Day 1 Classwork Introduction to Applications

This lesson takes the basics of percent and applies them to everyday problems. You will review important topics as well as learn how to solve these practical applications of percent.

Most percent word problems can be solved using the proportion:

partwhole

%

100

This important proportion will be adjusted for each of the problem types that follow.

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 usually given to waiters, valet, caddies, drivers and bellboys. ____________~ Commission: The amount of money earned by a salesperson for selling a certain product. _

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

_________________ _

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._____ 4) Even though I bought $10 worth of pencils, I had to pay $10.88._____ 5) 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 $65.25._____ 9) Phil only pays 50% because he is an employee. _____ 10) Will 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? _______Day 1 Homework Introduction to Applications

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.

a) Sales Taxb) Tipc) Commissiond) Discount

a) Sales Taxb) Tipc) Commissiond) Discount

Neat Fact

“Percent” comes from the Latin Per Centum.

The Latin word centum means 100, for example a century is 100 years.

_____ 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.

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?

14) Hahn had $25 left in her purse after shopping and spending 20% of her money. How much did she leave to go shopping with?

15) Ramon spent 60% of his $437 paycheck on gifts for his friends. How much did he spend?

_____________________________________________________________________________Review:

16) |4 – 62| 17) 4x + 6 – 21x = 91 18) Factor: 19) Solve: -12x – 16y 3x – 7 ≤ 29

Day 2 Classwork Tax and Tip

Tax – Add to the original price for the total cost. Tip – Add to the original bill for the total cost.

Money is always two decimal places (rounded to the nearest hundredth)Example:1) Suzy just bought the new laptop. It was $459 plus 8% sales tax. How much was her total purchase?

There are two ways to solve this problemMethod 1:

Find out what is 8% of $459

–––––– = ––––––

Then add it to the original

Item price + Tax = Grand total

_________ + _________ =

2) A sweatshirt at Hollister costs $60 and the rate of tax is 9%. How much is the tax?

3) After eating lunch at Applebee’s, the cost is $35. If you want to leave the waiter a 20% tip, how much money should you leave as a tip?

3) A 65 inch 3D-HDTV costs $1600. If the tax is 8.5%, what is the total?

4) 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?

5) Mrs. Aronow goes on a jet skiing tour while on vacation. The company charges $199 and 6.25% in tax. After the tour, she gives the instructor a 15% tip on her debit card. How much did the whole excursion cost?

Day 2 Classwork Tax and Tip

Extra Practice - Deconstructing Way

Mary buys $75 coat that has 8% tax. What is the final price of the coat?

Since it is asking for the final price you are paying 100% for the coat + 8% for tax That means you are paying 108%

Method 2:

The price of the item is 100%

AND tax is 8%

100% + 8% = 108%

108% • $459 = $495.72

This is the grand total

You must now change the percent to a decimal 108 % = 1.08

Take the coat price and multiply by the decimal 75 (1.08)

Your final price is $81

Examples:

1) A book at Barnes and Nobles cost $40 with 8% tax. Find the final price.

2) Michelle purchased a cd which was selling for $15. The tax was 7%. How much was the total cost?

3) Emily and her friends went to dinner and left a 5% tip for her waitress. If her bill was $25.00, how much did they pay in total?

4) A small business buys a computer system for $850 and pays a sales tax that is 5% of the cost. What is the final cost of the computer system?

5) Lori bought a turtle for $8.00, two goldfish for $1.00 each, and a snail for $0.50. There was 8.5% tax. What is the final cost at the store?

6) Ashley and her family went out to dinner. Their bill came to $40.00. If Ashley’s dad would like to leave a 20% tip and there is 8% tax, how much was their whole bill?

7) A dinner costs $60.75. There was 7.5% tax and the family wanted to leave a 15% tip. How much is the final bill?

Day 2 Homework Tax and Tip

**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.

3) 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?

4) 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?

5) You and a friend go out for dinner and spend $77.16. 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?

6) A new phone costs $399.00, if tax is 7.5%, what is the total cost of the phone?

7) Bryce bought an aquarium priced at $90.70. Shipping and handling cost him an additional 20%. What was the total cost of the aquarium, including shipping and handling?

8) Lynda was a horrible waitress. She spilled a drink on you and she brought you the wrong food. The bill came to $56.35 so you left her $3. What was the percent of tip you left her?

9) Sancho and his friend went to dinner at Chili’s. Their meal cost them $27. Tax was 9% and they left an 18% tip. What was the grand total Sancho charged to his credit card?

Day 3 Classwork Commission

Commission – You get a part of your sales.Example: if you sell $300 of products and receive a 10%

commission, you get ____ dollars.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1) Ms. Pickford works at Game Stop in her spare time. She earns an 8% commission for all sales. She sold $1500 in the month of November.

a) What was her commission?

b) If Ms. Pickford 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?

Try These: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?

Day 3 Classwork Commission

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.

Challenge5) While on vacation in Spain, a group can rent bicycles and scooter by the week. They get a reduced rental rate

if they rent 5 bicycles for every 2 scooters rented. They reduced rate per bicycle is $15.50 per week and the reduced rate per scooter is $160 per week. The sales tax on each rental is 12%.

a) The group has $1600 available to spend on bicycle and scooter rentals. What is the greatest number of bicycles and the greatest number of scooters the group can rent if the ratio of bicycles to scooters is 5:2?

b) If they do rent the greatest possible amount for each, they sales clerk will earn a 7% commission of the final price. What will the commission be?

Day 3 Commission Homework

1) If Drew’s sales for one week totaled $ 1500, and his commission on those sales totaled $82.50, then what is the percent of commission he received?

2) 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?

3) Renee works in the shoe department at Saks 5th 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? (Base + Commission : Total Salary)

4) 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?

5) What is the commission percentage paid on a $450 diamond necklace if you make $50?

6) 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?

7) 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?

8) 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.

Day 4 Classwork Discount

Example:You are buying a pair of sweats from Abercrombie & Fitch for $50. They are on sale for 20% off.

Option 1:1) Find the discount, by setting up a proportion. = Original Price

Discount: 1

Difference:

2) Subtract the discount from the original price,this will give you the SALES PRICE.

3) Find the tax if necessary, via a proportion.4) Add the tax to the SALES PRICE, this will

give you the final cost.

Option 2:20% off means that you are paying 80% of the total cost.

100% - 20% = 80%

So, to find the sale price, you multiply the cost by the percentage you are paying

$50 • 80% 50 • .80 = 40

The sale price of the sweatpants is $40.

––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––1) A HD-DVD player has a list price of $200 and is discounted 25%. a) How much would the savings be? (discount) b) What is the sales price?

c) If the tax is 8%, how much tax should they pay? d) What is the total cost of the DVD player?

2) The new Batman DVD costs $19.90. If you found it on sale at Kmart for 30% off the original price, how much does the DVD now cost?

3) American Eagle is having a sale on jeans. The original price was $49.50. The sale price is $33.00. What percent discount was taken? (percent of decrease)

Day 4 Classwork Discount

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 better deal?

= Original Price

Discount: 1

Difference:

5) A coat is currently $139.99. 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?

6) 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?

7) 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?

8) An XM radio player that lists for $398 in on sale for 30% off the list price. How much money do you save?

9) A Skateboard is reduced 25% in price in a sale. The old price was $120. Find the new price.

Day 4 Classwork Discount

1) The list price on a winter coat is $60. It is being sold at a 25% discount. What is the final price of the coat?

2) The regular price of an iPod is $480. It is on sale at a 35% discount. What is the sale price of the iPod?

3) A $135 snowboard was sold for 10% off. What was the total cost of the snowboard?

4) A Sweatshirt normally costs $22. This week it is on sale for 25% off the original price. What is the sale price of the sweatshirt?

5) A cowboy hat is regularly priced at $42. It is on sale for 15% off of the regular price. What is the final price?

*** Challenge***6) A bottle of lotion is $25. The lotion is 20% off but you must pay 8% tax. What is the final price?

Day 4 Homework Discount

1) A Laptop is on sale for 20% off the regular price. The price was originally $879.00. 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 (before tax)?

5) Last year there were 260 7th graders at Sequoya. 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?

6) Ben wants to buy a stereo. The regular price of the stereo is $420. The sale Best Buy is having says you can get $25 off for every $100 worth of merchandise purchased. He also has a coupon 25% off of the regular price. a) What is the sale price of the stereo?

b) What is the price of the coupon if he used the coupon instead?

c) Ben must pay 7.25% sales tax in addition to the lower price of the stereo. What is the total amount Ben must pay for the stereo?

Day 5 Classwork Simple Interest

Interest = (principal)(rate)(time)

Steps:

1) Change the rate (%) to a decimal.

I = (p)(r)(t)

2) Make sure the time is in years.3) Write I=, P=, R=, T=4) Substitute each value into the equation (with PARENTHESIS)5) Solve.

p is the principle. The money borrowed or invested.

r is rate. Rate is a percentage. You must change the percent to a decimal to solve the problem.

t is time. Time is in years. If it is in months, you must convert it to years to solve the problem.

1) Change each percent to a decimal

A) 24% B) 159% C) 8.4% D) 0.56% E) 21 1

2 %

2) Change months to years

A) 6 months B) 9 months C) 18 months D) 24 months

3) Mrs. Hochmuth deposited $200 in a bank that pays 5% simple interest.

How much will she earn in three years?

4) Suzy invested $500 at 8% simple interest.

a) What does the investment pay in 6 months? b) How much total money does she now have?

Day 5 Classwork Simple Interest

5) If you buy a car for $19,000 at an interest rate of 4.5% for 5 years, how much are you actually paying for the car?

6) If you buy a car for $20,000 at an interest rate of 3% for 5 years, what is the simple interest?

7) You invest $1,500 for three years. Find the amount of simple interest you earn at an annual rate of 6.25%?

*8) Suppose you invested $1200 for four years. You earned $312 in simple interest. What is the interest rate?

9) If you buy a house for $525,000 at an interest rate of 7% for 15 years, how much are you actually paying for that house?

Day 5 Homework Simple Interest

1) What is a reasonable estimate of the amount of money you will earn on $595 invested at 9% simple interest for 2 years?

2) Explain whether you would earn more money from Plan A or Plan B.

Plan A: $1,500 for 7 years at 8% Plan B: $1,500 for 8 years at 6%

3) Connor agreed to pay back a loan in 3 years at a simple interest rate of 15% on $2500 he borrowed.

What is the total he must pay back?

4) Taylor borrowed $1200 at a simple interest rate of 8.5% for 6 months. How much interest did she owe?

5) $895 was invested for 2 years at 10% interest. How much total money do you have after the 2 years?

6) How much money is earned if $50 is invested at 17.5% simple interest for 2 years?

7) What would you have to repay if you borrowed $700 at simple interest for 3 years at 6%.

Day 5 Homework Simple Interest

8) What is the interest if $4500 is borrowed at 9.5% simple interest for 2 years 6 months?

9) Courtney borrowed $500 from the bank. She was charged her 9% interest per year. The loan was for 2 years,

how much does she have to pay?

*10) Sydney borrowed $1200 at a simple interest rate for 6 months. If the interest was $51 what was the rate of interest?

Extended Response:

11) If you buy a house for $450,000 at an interest rate of 6% for 30 years.

a) What is the interest?

b) How much will you actually be paying for the house?

c) What will your monthly payment be?

d) How much money would you save if you took out the loan for 15 years?

e) Why might a person take out a 30 year loan instead of a 15 year loan?

Extra Practice

Using the deconstructing method solve each problem:

1) A customer wants to tip 15% on a restaurant bill that is $35. What will be the total bill with tip?

2) Mark wants to buy exercise equipment that costs $140 and the sales tax is 8.5%. What is the

total cost of equipment?

3) Emily is buying a Bike. The total for the Bike is $240. Emily has a 30% off coupon. How much is the sale price?

4) Ryan wants to tip his taxicab driver 20%. If his commute costs $15, what is the total cost?

5) Find the total cost of a spa treatment of $42 including 6% tax and 20% tip.

**** Challenge****

6) Melissa bought a $120 necklace. She used a 20% off coupon and had to pay 7% tax. What was her final total of the necklace?

7) When you have a commission question and you decide to use the deconstruction method to solve it why would you always get a decimal with no whole number 1. (example 0.25). Explain why a commission question doesn’t start with 100%.

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________