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FUNDAMENTALS!DISCIPLINE!

!BLUE!BELT!TRAINING!

PERCENTS!!

NAME_______________________________!

Blue Belt Order of Mastery

1. Converting fractions, decimals, and percents 2. Understanding the meaning of percents 3. Percents as proportions 4. Percent change (increase/decrease) 5. Solving percent applications 6. Simple and Compound Interest

Percent!Review!&!Practice!

After you finish this belt, you might feel a bit of déjà vu; that is, you might be thinking I have done this before. You would be right! A percent is nothing more than a fraction in a different form. If you had a ½ of a dollar you would have .50 cents or 50% of a dollar. Or, another example, if there were 28 people in your math class and 10 people out of 28 wore glasses….that would equal, .357 of the people or 35.7% of the people. The Point? A Fraction equals a Decimal equals a Percent….in fact, we say this important thing when working with Percents: A Percent is a Decimal in Disguise. Whenever you see a Percent convert it to a decimal to use in your calculations. Why would you do this? Because Percent literally translated means “part of a hundred” or “part of a whole”. Which you know from the Yellow Belt is the definition of a Fraction. Of course, you know that a decimal can be converted to a fraction by using the decimal place value system. A Percent is nothing more than a decimal that has been multiplied by a 100 .78 78%

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! !!We see percents all the time in the news and the world around us. The United States has raised taxes by 3% or Lebron James is shooting 65% from the free throw line. You’ll see a lot of math problems asking you to solve percents as they apply to real world situations. Most likely, you know how to deal with percents using the proportion method which is a good way but now that you are in algebra, you should think about using the Equation Method; both detailed below.

Example: 40% of high school graduates in a certain high school chose to enlist in the military. If 128 in a high school went into the military, what is the number that graduated from the high school?

Proportion!Method! ! ! ! ! ! Equation!Method! ! !

40100

!128

x ! ! ! ! ! ! ! %(Whole)=!Part!

! ! ! ! ! ! ! ! .40(Whole)=!128!Cross!Multiply!! ! ! ! ! ! Whole!=!!128!/!.40!40x!=!12800!

!!x!=!320! ! ! ! ! ! ! ! x!=!320!!!!

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X!100

"!100!

Basically,!the!definition!of!a!fraction!!part/whole!rearranged!into!a!multiplication!problem!

First,!Grasshopper,!you!must!become!a!master!of!changing!the!forms!of!fractions,!decimals!and!percents!!!Remember,!they!are!all!equal!to!each!other!just!converted!into!different!forms.!Write each percent as a fraction in simplest form. 1. 99%

2. 75%

3. 30%

Write each percent as a decimal. 4. 96.5%

5. 79%

6. 90.8%

Write each decimal as a percent. 7. 0.60

8. 6.25

9. 0.059

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Write each fraction as a percent. Round to the nearest hundredth of a percent. 10. 4

5

11. 3

5

12. 16

25

13. 1

10

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Write each fraction as a percent. Round to the nearest hundredth of a percent. 14. 7

10

15. 173

25

16. 9

22

17. 1

2

Complete the Table- (You’ve seen this before) Fraction Decimal Percent

18. 916

19. .44

20. 2518

21. 15%

22. 42%

23. 5.75

24. 2.4%

25. 3 45

Finding a Percent of a Number is finding the Part of the number; that is, the Part " Whole. These problems will give you two of the three pieces: Percent, Part, or whole. Your job is to find the other by identifying what you have been given. Use the Definition of a Fraction Rearranged- % (Whole) = Part 26. 96% of 15.9 27. 78% of 365 28. 85% of 5.8 29. 133% of 89 30. 12% of 1.3 31. 60% of what number is 36? 32. What percent of 536 is 335? 33. 43% of 389 is what number?

34. Kevin won 89 percent of his wrestling matches this year and came in third at the state tournament. If he competed in 34 matches over the course of the season (including the state tournament), how many did he lose?

35. Abigail is a good scorer for her soccer team. She scored 17 goals during regular play, and she scored 3 on penalty kicks. What percent of her goals did not result from penalty kicks?

36. Nicholas hit a home run that went 328 feet on Saturday. On Monday, he hit one that went 316 feet. The distance of the second home run was what percent of the first home run?

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Percents!in!Algebra!(Never!let!the!salesman!fool!you)!

Using the Proportion Method to Solve Percent Problems

There are a variety of ways to solve percent problems, many of which can be VERY confusing. Fortunately, the PROPORTION METHOD will work for all three types of questions:

1. What number is 75% of 4? 2. 3 is what percent of 4? 3. 75% of what number is 3?

Using the PROPORTION METHOD, the set-up is always the same:

100percent

ofis!

EXAMPLE #1: What number is 75% of 4? (or Find 75% of 4.)

The PERCENT always goes over 100. (It's a part of the whole 100%.)

4 appears with the word of: 10075

4!

is

It's the WHOLE and goes on the bottom.

We're trying to find the missing part IS (on the top).

In a proportion the cross-products are equal: So 4 times 75 is equal to 100 times the PART.

The missing PART equals 4 times 75 divided by 100.

(Multiply the two opposite corners with numbers; then divide by the other number.)

4 times 75 = 100 times the part

300 = 100 times the part

300/100 = 100/100 times the part 3 = the part

EXAMPLE #2: 3 is what percent of 4?

3 appears with the word is: It's the PART and goes on top. 4 appears with the word of:

It's the WHOLE and goes on the bottom.

We're trying to find the missing PERCENT (out of the whole 100%).

In a proportion the cross-products are equal: So 3 times 100 is equal to 4 times the PERCENT.

The missing PERCENT equals 100 times 3 divided by 4.

(Multiply the two opposite corners with numbers; then divide by the other number.)

3 times 100 = 4 times the percent 300 = 4 times the percent

300/4 = 4/4 times the percent 75 = the percent

EXAMPLE #3: 75% of what number is 3? (or 3 is 75% of what number?)

The PERCENT always goes over 100. (It's a part of the whole 100%.)

3 appears with the word is:

It's the PART and goes on the top. 100753

!of

We're trying to find the missing WHOLE (on the bottom).

In a proportion the cross-products are equal: So 3 times 100 is equal to 75 times the WHOLE.

The missing WHOLE equals 3 times 100 divided by 75.

(Multiply the two opposite corners with numbers; then divide by the other number.)

3 times 100 = 75 times the whole 300 = 75 times the whole

300/75 = 75/75 times the whole 4 = the whole

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EXAMPLE #4: Find 83 2/3 % of 12.6 (or What number is 83 2/3 % of 12.6?)

The PERCENT always goes over 100. (It's a part of the whole 100%.)

1003283

6.12!

is

12.6 appears with the word of: It's the WHOLE and goes on the bottom.

We're trying to find the missing part IS (on the top).

In a proportion the cross-products are equal: So 12.6 times 83 2/3 is equal to 100 times the PART.

The missing IS equals 12.6 times 83 2/3 divided by 100.

(Multiply the two opposite corners with numbers; then divide by the other number.)

12.6 times 83 2/3 = 100 times the part

(126/10)(251/3) = 100 times the part 31626/30 = 100 times the part

(31626/30)(1/100) = (100/1)(1/100)( the part) 31626/3000 = the part 10542/1000 = the part 10.542 = the part

""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!CHEAT!SHEET!!When!I!say! ! ! ! ! This!is!how!you!figure!it!out! ! You!could!also!do!this!! ! ! ! ! ! (PROPORTION!METHOD)! ! !(ALGEBRAIC!METHOD)!!

39%!of!50!is!what!number?! ! !!!!!!!!10039 !=!

50x ! ! ! !!(.39)(50)!=!x! !

! ! !!

39!is!50%!of!what!number?! ! !!!!!!!!x

39 !=!10050 ! ! ! 39!=!(.50)x! ! !

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39!is!what!percent!of!50?! ! !!!!!!!5039 !!=!

100x ! ! ! 39!=!!x(50)! ! !

! !Remember!“is”!means!“=”!!and!“!of”!means!“multiply”!!

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!!Now!you!try!it:!1.!!How!much!money!is!35%!of!750?! ! ! 2.!!What!number!is!25%!of!80?!!!!3.!!What!number!is!200%!of!5?! ! ! ! 4.!!52!is!12.5%!of!what!number?!!!!5.!!42!feet!is!52%!of!what!length?! ! ! 6.!!90!is!45%!of!what!number?!!!!7.!!3!inches!is!what!percent!of!40!inches?! ! 8.!!55!years!is!what!percent!of!20!years?!!!!9.!!18!is!what!percent!of!60?! ! ! ! 10.!!$240!is!what!percent!of!$50?!!!!11.!Mr.!T.!is!going!to!put!an!island!in!his!kitchen.!(no,!not!a!real!island…it’s!the!kind!with!a!countertop!on!it)!

The!dimensions!of!his!kitchen!are!shown!below,!along!with!the!dimensions!of!the!island.!!What!percent!of!the!kitchen!does!the!island!take!up?!!

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!12. A!$120!coat!goes!on!sale!for!20%!off.!!What’s!the!new!price?!!!!13. Last!year!Miss!Vincent!was!given!a!3%!bonus!on!her!regular!yearly!salary.!!The!bonus!amounted!to!$720.!!What!

is!her!regular!yearly!salary?!!!!14. Jed!makes!a!2%!commission!on!each!case!of!mint!skittles!he!sells.!!When!he!sold!a!whole!case,!he!made!$2.!!

How!much!did!the!case!of!mint!skittles!cost?!!

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!!!!15. Fill!in!the!blanks!at!each!table!

Item! Original!Price! New!Price! %!!increase!

Skis! $220! ! 15!

Shoes! $30! ! !10!

Sandwich! $1.80! ! 5!

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Item! Original!Price! New!Price! %!!decrease!

Sweater! $60! ! 25!

Fly!rod! $20! ! 8!

Radio! $45! ! 5!

!16. You!want!to!buy!the!video!game!Call!of!Duty"!Black!Ops.!!At!Gamestop,!they’re!selling!it!for!$65,!but!it’s!on!sale!

right!now!for!10%!off.!!You!also!have!a!Gamestop!coupon!for!another!10%!off!the!sale!price.!!Your!friend!has!a!bootleg!copy!of!the!game!that!he’ll!sell!you!for!$65!as!well,!and!he’ll!give!you!20%!off.!!Does!the!game!cost!the!same!at!both!places?!!Why!or!why!not?!

!!!!!17. Nordstrom’s!has!a!coat!on!sale!for!30%!off!the!regular!price!of!$60.!!The!same!coat!is!on!sale!at!Macy’s!for!20%!

off!the!regular!price!of!$60.!!You!also!have!a!coupon!at!Macy’s!for!10%!off!the!sale!price.!!Will!you!save!money!by!going!to!Macy’s?!!Explain!why!or!why!not.!

M!!!!!!!!

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Measuring!Percent!Change!!Another!common!percent!problem!involves!percent!change.!!More!specifically,!percent!increase!or!percent!decrease.!!The!most!important!thing!to!remember!is!before!you!find!the!percent!change,!you!need!to!find!the!ACTUAL!CHANGE.!!Look!over!the!examples!below:!!PERCENT!CHANGE!PROBLEM!(DECREASE)!Ashley!saw!a!jacket!she!wanted!to!buy.! Last!week!she!couldn’t!afford!it!because!it!cost!$200.! But!they!discounted!the!price.! Now!it!only!costs!$125.!What!percent!discount!are!they!giving?!

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If the problem asks you to solve for the percent discount, then this is a ‘percent CHANGE’ problem. Here is how to solve this type of problem: ! Find the ACTUAL change FIRST. Original Price – New Price = Actual Change

$200 - $125 = $75 !

! PartWhole

!% ! ! ! ngePercentChaOriginal

geActualChan! !

The difference is the part: 75 The original is the whole: 200

100%

20075

! Cross multiply to get 37.5% PERCENT!DIFFERENCE!PROBLEM! (INCREASE)!Mr.!H.!makes!$40,900!a!year.!His!boss,!Ms.!Griswold!just!gave!him!a!raise.!Now!he!makes!$42,900!a!year.!His!salary!has!increased by what percent?!

"! Find the Actual Change between the new salary and the original salary: Original Salary - New Salary = Actual Change

$40,900 - $40,900 = $2,000

! PartWhole

!% !! ! ngePercentChaOriginal

geActualChan!

The difference is the part: 2,000 The original is the whole: 40,900

100%

900,40000,2

! Cross multiply and you get 4.9%

Actual!Change!is!the!difference!between!the!Old!and!the!New.!

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Now!you!try!!!Find!the!percent!change!of!each:!

1. From 40 inches to 37 inches 6. From $53 to $58

2. From 37 miles to 41.6 miles 7. From 56 ft to 22 ft

3. From 43 inches to 1 inch 8. From 60 ft to 18 ft

4. From 47 hours to 98 hours 9. From 63 m to 82.4 m

5. From 50 hours to 62 hours 10. From 66 grams to 79 grams

What’s the final price of each?

11. Original price of a book: $14.95 Discount: 28%

12. Original price of a car: $52,000.00 Discount: 50%

13. Cost of shorts: $44.95 Markup: 30%

14. Cost of a motorcycle: $3,500.00 Markup: 90%

15. Original price of a microphone: $169.95 Tax: 2%

16. Original price of a parrot: $200.00 Tax: 4% !!!

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Putting!it!into!words!1. Most!likely,!your!parents!have!a!checking!account.!!Most!checking!accounts!earn!about!1%!per!year!on!the!

balance.!!How!much!would!you!earn!if!your!checking!account!had!$1,250?!!!

2. You!decide!to!open!a!savings!account!that!pays!you!3.5%!interest!on!the!balance!per!year.!!How!much!money!would!you!have!at!the!end!of!one!year,!if!you!put!$850!in!the!account?!

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3. If!you!put!$1000!in!a!certificate!of!deposit!(CD),!and!at!the!end!of!1!year!the!CD!was!worth!$1150,!what!is!the!rate!of!return!(that!is,!the!percent!change)!in!your!investment?!

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4. Your!friend!keeps!hitting!you!up!for!lunch!money!each!day.!!You!finally!tell!him!that!you!will!loan!him!$5!but!you!will!charge!him!interest!at!a!rate!of!!.25%!per!day.!!After!6!days,!what!does!he!owe!you.!!(there!can!be!a!few!different!ways!to!figure!this!)!

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5. Great!News!!!Your!house!has!just!appreciated!(gone!up!in!value)!by!7.5%.!!What!is!the!value!of!your!house!if!your!parents!originally!purchased!it!for!$270,000?!

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6. Great!News!!!You!have!just!received!a!letter!in!the!mail!congratulating!you!that!you!have!just!been!pre"approved!for!a!credit!card!!!Now,!you!can!totally!customize!your!room!with!the!latest!gaming!and!surround!sound!speaker!system!to!be!the!ultimate!gaming!experience.!!You!charge!$3500!on!the!credit!card.!!The!bank!then!charges!you!22%!interest!on!your!monthly!balance.!!Assuming!you!pay!nothing!on!it!each!month!(hey,!you!don’t!earn!money!and!noone!pays!you!for!all!the!work!you!do!at!school),!what!do!you!owe!on!your!credit!card!each!of!the!first!3!months?!!(roll!in!the!interest!accrued!into!the!following!months).!

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7. Being!the!savy!investor,!you!decide!to!invest!$12,000!into!Jamba!Juice!Stock.!!After!one!year,!your!investment!has!grown!to!$16,500.!!What!is!the!percent!change!in!your!investment?!

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8. Holy!Toledo!!!I"Pod!ownership!has!grown!to!3.5!million!up!from!800,000!in!2005.!!What!is!the!percent!change!in!ownership?!

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9. You!have!probably!noticed!your!parents!are!a!little!down.!!It!is!because!their!retirement!investments!have!dropped!recently!by!8%.!!What!is!the!value!of!their!portfolio!if!it!was!worth!$350,000!before!the!drop!in!the!stock!market?!

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10. Your!parents!are!helping!your!save!for!college!by!investing!in!529!college!savings!plan!for!you.!!If!they!invested!$3000!last!year!and!it!was!now!worth!$3710!today,!how!much!has!it!grown?!!By!what!amount!and!by!what!percentage!rate?!

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11. Real!Estate!Boom!!!A!few!years!ago,!your!parents!bought!a!small!home!in!O.B.!for!$275,000.!!Now,!to!their!delight,!it!is!worth!$825,000.!!What!was!the!return!on!the!investment?!!(what!was!the!actual!gain!and!of!course!percentage!gain).!

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12. Due!to!the!launching!of!the!I"Phone,!you!decided!to!buy!Apple!stock!at!a!$105!per!share.!!A!year!later,!the!price!of!Apple!stock!was!at!$165!per!share.!!What!is!the!percentage!growth!in!the!stock?!!!

! ! Part!II:!!Assuming!you!bought!200!shares,!what!is!the!growth!in!your!investment?!!!! ! Part!III:!!You!project!4%!growth!in!the!next!year.!!What!is!your!portfolio!worth?!

13. Jason paid $44.10 for a wireless phone after a thirty percent discount was applied to the price. What was the original price of the wireless phone?

14. The EdHelper Supermarket is donating two percent of this month's sales to the local high school. If the high school hopes to raise $920 this month, how much sales will the supermarket need to have to reach the goal?

15. The football team spent $8,560, which was seven percent more than they had budgeted. How much did the team budget to spend?

16. In Timothy's algebra class, Timothy scored 89% on the exam by answering seventeen questions correctly. How many questions did Timothy answer incorrectly?

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Mixing!it!Up!ANSWER!THE!FOLLOWING!WORD!PROBLEMS.! EACH!QUESTION!IS!EITHER!A!‘PERCENT!OF’!OR!A!‘PERCENT!DIFFERENCE’!PROBLEM.! IN!THE!‘PERCENT!DIFFERENCE’!PROBLEMS!I!HAVE!HIGHLIGHTED!KEY!WORDS!THAT!TELL!YOU!WHAT!KIND!OF!PROBLEM!IT!IS.! ROUND TO THE NEAREST PERCENT OR WHOLE!NUMBER.!!

1.!!! Jessica!enjoys!playing!disk!golf.!She!has!really!improved!in!recent!months,!and!she!got!her!lowest!score!ever!today.!She!scored!a!19!on!a!nine"hole!course.!She!remembered!last!year!when!she!played!the!same!course!for!the!first!time!and!scored!a29.!By!what!percent!did!her!score!decrease!this!last!time!compared!to!the!time!she!scored!a!29?!

!2.!!! In!Doug’s!Calculus!class,!Doug!scored!80%!on!the!exam!by!answering!63!questions!correctly.!

How!many!questions!did!Doug!answer!incorrectly?!!

3.!!!According!to!the!statistics,!the!Chargers!have!scored!17%!of!their!touchdowns!in!the!first!half.! If!they!scored!a!total!of!12!touchdowns!in!the!first!half!this!year,!about!how!many!did!they!score!in!the!second!half?!

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4.!!!Alexis!ran!the!100"meter!dash!in!14.05!seconds!yesterday!at!track!practice.! Then!today!she!ran!it!in!13.55.!!By!what!percent!did!her!time!decrease?!

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!5.!!!Mr.!H.!got!a!raise!! Last!year!he!made!$43,000!a!year,!and!now!this!year!he!makes!$47,000.!

What!percent!raise!did!he!get?!!!

6.!!!When!our!teacher!handed!out!our!math!test,!she!told!us!to!omit!problems!4,!7,!9,!10,!11,!and!15.!There!were!80!problems!on!the!test.!What!percent!of!the!problems!did!we!have!to!solve?!

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7.!!!Mr.!T.!bought!his!brother!a!Chargers!jersey!for!his!birthday.! It!cost!him!$120.! Then!yesterday!he!saw!it!on!sale!for!$90.! By!what!percent!did!they!decrease!the!price?!

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8.!!! Jimmy!got!a!raise!from!$6.00!an!hour!to!$8.00!an!hour.! This!was!a!raise!of!what!percent?!!!

9.!!!A!cookbook!was!reduced!from!$24.50!to!$17.95.! This!was!a!reduction!of!what!percent?!!!

10.!Sarah!earns!$1800!a!month!and!pays!$430!for!rent.!What!percent!of!her!income!goes!for!rent?!!!

11.!Janet's!salary!is!$400!a!week,!and!she!pays!$53!in!taxes.!What!percent!goes!for!taxes?!!!

12.!Janet's!salary!increased!from!$400!a!week!to!$440.! This!was!an!increase!of!what!percent?!!!!

13.!A!sweater!was!marked!down!from!$40!to!$30.!This!was!a!difference!of!what!percent?!!!!

14.!A!population!grew!from!100,000!in!1980!to!116,000!in!1990.!This!was!a!difference!of!what!percent?!

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Mastering Percents….Practice Makes Perfect WRITE AS A FRACTION IN SIMPLEST FORM 1. 25% 2. 40% 3. 37 ½ % 4. 85% 5. 60% 6. 66 2/3 % 7. 72% 8. 16% 9. 4% 10. 2 ½% 11. 360% 12. 150% 13. 32% of 300 is what number? 14. 6% of 145 is what number? 15. 1% of 3200 is what number? 16. 6 ¼% of 500 is what number? 17. % of 12 is what number? 18. 9.2% of 180 is what number? 19. 8.1% of 250 is what number? 20. 110% of 30 is what number? 21. 8 is 20% of what number? 22. 15 is 25% of what number? 23. 21 is 6% of what number? 24. 99 is 180% of what number? 25. 4.2 is 75% of what number? 26. 32.4 is 45% of what number? 27. What percent of 45 is 7.2? 28. What percent of 3 is 150? 29. What percent of 150 is 3? 30. What percent of 3 is 150? 31. What percent of 250 is 50? 32. What percent of 50 is 250? Complete the tables below. Original

Original Price %

Discount

Price Decreased

New Price Original

Price

% Markup

Price Decrease

d

New Price

33. $12 25% $_______ $_____ 37. $44 25% $______ $_____ 34. $18 20% $______ $_____ 38. $85 20% $______ $_____ 35. $75 10% $_______ $_____ 39. $160 30% $______ $_____ 36. $240 15% $______ $_____ 40. $25 6% $______ $_____

Amount Invested x Annual Interest Rate = Annual Simple Interest 41. $400 7.5% = $______________ 42. $60,000 9.5% = $______________ 43. $1,000 _______% = $105 44. $2,500 ________% = $275 45. $________ 7.25% = $870

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Perplexing!Percentage!Problems!Be!careful!with!these!!!Make!sure!you!know!which!will!be!your!whole!and!which!will!be!your!part!and!pay!close!attention!to!what!the!problem!is!asking!you!for….often,!once!you!find!your!part!you!have!to!add!or!subtract!from!your!whole!to!get!your!answer.!

!Complete.!!

1.!!!Ana!Maria!has!applied!for!United!States!citizenship.!She!has!studied!American!history!and!government!for!a!long!time!and!thinks!she!is!ready!to!take!the!citizenship!test.!When!she!took!the!practice!test!online!she!answered!fifty"two!questions!correctly!and!only!missed!five.!What!percent!of!the!questions!did!she!get!right?!

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2.!! A!particular!species!of!bird!weights!about!thirty"two!grams!when!born.!If!its!weight!increases!by!seven!percent!a!day,!how!much!will!it!weigh!on!the!fourth!day!of!its!life?!

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3.!!!Scientists!estimate!that!the!average!annual!temperature!in!Bigtown!has!increased!by!two!and!six!tenths!percent!over!the!past!century.!If!the!current!average!annual!temperature!in!Bigtown!is!17.5 C,!what!must!the!average!temperature!have!been!100!years!ago?!Round!your!answer!to!the!nearest!hundredth!of!a!degree.!

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4.!! Ms.!Davis!wants!to!donate!nine!percent!of!her!paycheck!to!the!Mountain!Springs!Hospital!for!Children.!If!her!paycheck!is!$867.00,!how!much!should!she!send!to!the!Mountain!Springs!Hospital!for!Children?!

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5.!!!Sarah's!mother!is!a!nurse.!She!came!to!school!to!check!our!posture!and!our!backs.!She!told!us!that!about!4.8%!of!children!have!a!problem!called!scoliosis.!There!are!two!hundred!eight!students!in!our!school.!If!our!school!is!like!the!average,!how!many!children!will!have!scoliosis?!Express!your!answer!to!the!nearest!whole!number.!

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6.!! Connor!collects!aluminum!cans!and!takes!them!to!the!recycling!center!every!week.!He!put!recycling!boxes!in!all!the!classrooms,!the!cafeteria,!and!the!teachers'!lounge.!He!put!a!sign!on!each!box!asking!people!not!to!put!anything!but!aluminum!cans!in!them.!Every!week,!though,!Connor!finds!objects!other!than!aluminum!cans!in!the!recycling!boxes.!He!estimates!that!ten!percent!of!the!weight!of!the!material!in!the!boxes!is!non"recyclable!junk.!The!total!weight!of!all!the!items!collected!in!the!recycling!boxes!this!week!was!one!hundred!forty"one!pounds.!What!was!the!weight!of!the!aluminum!cans,!rounded!to!the!nearest!tenth!pound?!

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Complete.!!

7.!!!The!voice!on!the!phone!was!yet!another!creditor.!His!coarse!voice!and!rudeness!began!to!infuriate!me.!"Just!how!much!do!I!owe?"!I!demanded.!He!replied,!"You!owe!$717.63!on!your!credit!card.!We!will!have!to!add!a!past!due!charge!of!$24,!an!over!limit!fee!of!$25,!and!a!service!charge!of!7%!of!the!amount!owed!on!the!credit!card."!I!told!him!I!would!send!a!check!for!the!full!amount!immediately.!For!how!much!should!the!check!be!written?!

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8.!! Let's!say!you!have!a!molecule!that!is!made!entirely!out!of!four!different!kinds!of!subunits!called!As,!Ts,!Cs,!and!Gs.!In!this!molecule,!the!number!of!Cs!equals!the!number!of!Gs!and!the!number!of!Ts!equals!the!number!of!As.!If!one!of!these!molecules!is!analyzed!and!found!to!consist!of!31%!As,!then!what!percent!of!the!molecule!is!made!up!of!Gs?!

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9.!!!There!were!18,288!weddings!in!Springs!City!last!year.!According!to!state!records,!notaries!public!performed!16%!of!the!weddings.!How!many!weddings!were!not!performed!by!notaries!public?!

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10.!! Mr.!Snead!makes!$32,900!a!year.!His!boss,!Ms.!Tong!just!gave!him!a!raise.!Now!he!makes!$36,900!a!year.!His!salary!has!increased!by!what!percent?!Round!your!answer!to!the!nearest!tenth!of!a!percent.!

11.!!!Mushrooms!produce!a!tremendous!number!of!spores.!However,!very!few!spores!go!on!to!establish!a!new!mushroom!colony.!A!"colony"!is!actually!a!little!bunch!of!fuzzy"looking!cells!called!a!mycelium.!Let's!say!a!particular!mushroom!produces!a!billion!spores!in!a!day.!If!one"sixth!of!one!percent!of!those!spores!successfully!produces!a!new!mycelium,!how!many!of!the!spores!were!successful?!

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12.!! Edgewater!Elementary!School!recently!participated!in!a!survey!done!by!the!local!university.!The!College!of!Education!had!made!an!arrangement!with!our!principal!for!the!survey.!They!wanted!to!determine!if!students!thought!male!teachers!or!female!teachers!were!more!lenient.!32%!of!the!students!thought!female!teachers!were!more!lenient,!14%!said!they!were!the!same,!6%!had!no!opinion,!and!the!rest!of!the!students!said!male!teachers!were!more!lenient.!On!the!day!of!the!survey,!there!were!four!hundred!fifty!students!at!school.!How!many!said!male!teachers!were!more!lenient?!

!13. !Last!week,!Chris!bought!a!DVD!for!$10.80!while!the!store!was!having!a!25%!off!sale.!!The!sale!is!now!over.!!How!

much!would!the!same!DVD!cost!today?!!!!

14. Which!is!greater,!73!percent!of!87!or!87!percent!of!73?!Explain!your!answer.!!!!!!!!15.!!The!original!price!of!doo"dads(I!know!it!is!not!a!real!object)!this!year!is!$2.60.!!If!the!price!of!doo"dads!next!year!goes!up!by!5%!more!than!this!year’s,!what!will!be!it’s!price?!!If!the!price!then!dropped!5%!the!year!after!that,!show!that!the!price!would!not!return!to!its!original!price!of!$2.60?!!Explain!that!apparent!paradox.!

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Interest: It’s both Simple and Compound

In the real world, most people can’t afford to buy things like cars and houses with cash. So we need to get a loan from a bank, or use credit cards to purchase items we don’t have enough money for. The only problem is, when you get a loan, you have to pay back a lot more than you borrowed. The banks charge interest, and there are two main kinds: Simple or Compound. SIMPLE INTEREST

Basically, simple interest is interest paid on the original PRINCIPAL only. The PRINCIPAL is the amount you borrowed. It’s the money you start with. Then there’s the interest RATE. That’s the percent that you’ll be paying in addition to the principal. Then there’s the TIME of the loan. That’s how many years you have until the bank makes you pay it back. For a car that’s usually 5 years. For a house, it can be up to 30 years. So for simple interest you can put all those things into a formula: I = prt I = the amount of interest you pay p = the principal, or the money you start with r = the rate, or the percent that you pay t = the time, the amount of years you have to pay it off For example, say you got a loan for $10,000 to buy a car. The interest rate they gave you was 8%. How much interest will you have to pay after 5 years? Just plug it into the formula: I = p× r × t p = 10,000 r = .08 (8%) t = 5 I = (10,000)(.08)(5) I = 4,000 So over the course of 5 years, you’ll have to pay $4,000 in interest! Ouch! You borrowed $10,000 and you owe $14,000 back! But it gets even worse with COMPOUND interest COMPOUND INTEREST This type of interest changes every year. In other words, at the end of each year, the interest earned is added to the original amount and then you’re charged interest on that new total. So if we used the above example and used compound interest instead, it’d look like this: Interest for the first year: I = (10,000)(.08)(1) I = 800 So now your new principal is 10,000 + 800 which equals 10,800 For the second year the formula then changes with a new principal: I = (10,800)(.08)(1) I = 864 Now the principal is 10,800 + 864 = 11,664. You have to keep doing that each year until you reach your total. In our case that’s 5 years, so our total interest would end up being $4,693, a lot more than simple interest! The good news is, they do this for investments as well. That means you can put money in a savings account and depending on whether you’re earning simple interest or compound interest, you’ll make a completely different amount….so it’s good to know what they mean.

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Your turn! Consider the following to be loans with Simple Interest. Calculate how much interest you’d be paying for each: 1. $35,000 at 9% for 2 years 5. $210 at 13% for 5 years 2. $19,000 at 8% for 7 years 6. $370 at 8% for 3 years 3. $470 at 8% for 6 years 7. $1,520 at 2% for 3 years 4. $39,000 at 6% for 3 years 8. $1,080 at 13% for 2 years Now let’s try some Compound Interest: (if it says semi-annual that means you’re doing it twice a year. Ouch!) 9. $56,000 at 3% compounded annually for 9 years 10. $190 at 2% compounded annually for 5 years 11. $35,000 at 13% compounded semiannually for 5 years 12. $29,900 at 5% compounded semiannually for 2 years 13. $24,700 at 13% compounded semiannually for 2 years 14. $42,800 at 5% compounded semiannually for 4 years 15. $37,600 at 13% compounded semiannually for 9 years 16. $32,500 at 5% compounded semiannually for 2 years

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ANSWERS- Blue Belt Packet Fundamentals- Percents Percent Review & Practice 1. .99 2. ¾ 3. 3/10 4. .965 5. .79 6. .908 7. 60% 8. 62%% 9. 5.9% 10. 80% 11. 60% 12. 64% 13. 10% 14. 70% 15. 692% 16. 40.91% 17. 50% 18. .5625, 56.25% 19. 11/25, 44% 20. 1.38, 138% 21. 3/20, .15 22. 42/100, .42 23. 5 ¾, 575% 24. 3/125, .024 25. 3.8, 380% 26. 15.264 27. 284.7 28. 4.93 29. 118.37 30. .156 31. 60 32. 62.5% 33. 163.4 34. 30.26 35. 70% 36. 96.3% Percents in Algebra- Never Let the Salesman Fool You 1. $262.50 2. 20 3. 10 4. 416 5. 81 6. 200 7. 7.5% 8. 275% 9. 30 10. 480% 11. 42% 12. 96 13. $24,000 14. 100 15. $253, $33, $1.89, $45, $18.40, $42,75 16. No, Gamestop costs $52.65, your friend costs $52.00 17. No Nordstroms costs $42, Macy’s costs $43.20- Measuring Change Through Percents

13. $58.44 14. $6,650.00 15. $173.35 16. $208.00 !Putting it into Words 1. 12.5 % 2. $879.75 3. 15% 4. Day 1: $6.25, Day 2: $7.81, Day 3: $9.76 5. $290,250 6. 1st Month: $3500+$770= $4270 2nd Month: $4270 + $939.40 3rd Month: $5,209 + $1,145.98=$6,354.98 7. 37.5% 8. 337.5% 9. -$28,000 value is $322,000 10. +$710, 23.6% 11. $550,000, 200% 12. 57%, $12,000 profit, $1,320 + $33,000= $34,320 13. 63 14. 46,000 15. 8000 16. 3 Mixing it up 1)! 34%! 2)! 79!Questions!3)! 59!Touchdowns! 4)! 4%!5)! 9%! 6)! 93%! 7)25%! 8)33%! 9)!27%! 10)!23%! 11)!13%! 12)!10%! 13)!25%! 14)! 16%!

Mastering Percents- Practice Makes Perfect 1. ¼ 2. 2/5 3. 37 ½ % 4. 17/20 5. 3/5 6. 33/50 7. 18/25 8. 4/25 9. 2/50 10. 2 1/5 11. 3 3/5 12. 1 ½ 13. 96 14. 8.7 15. 32 16. 31.25 17. .06 18. 16.56 19. 20.25 20. 33 21. 40 22. 60 23. 350 24. 55 25. 5.6 26. 72 27. 16% 28. 5000% 29. 2% 30. 5000% 31. 20% 32. 500% 33. 3, 9 34. 3.6, 14.40 35. 7.5, 67.5 36. 36, 204 37. 11, 55 38. 17, 102 39. 48, 208 40. 1.5, 26.5 41. 30 42. 5,700 43. 10.5% 44. 11% 45. $850 46. $12,000 Perplexing Percentage Problems

1. 91 % 2. 41.95 grams 3. 17.06 degrees Celsius 4. $78.03 5. 10 children 6. 126.9 pounds 7. $816.86 8. 19 % 9. 15,362 10. 12.2 % 11. 1,666,667 12. 216 students 13. $14.40 14. They both equal 63.51 because they are a part of each other’s whole. 15. $2.73 the first year then it drops to $2.59; one cent less. This happens because different wholes.

Interest: It’s Simple and Compound 1. $41,300.00 2. $29,640.00 3. $695.60 4. $46,020.00 5. $346.50 6. $458.80 7. $1,611.20 8. $1,360.80 9. $73,067.30 10. $209.78 11. $65,699.81 12. $33,004.01 13. $31,775.72 14. $52,147.64 15. $116,810.20 16. $35,873.92

1. 7.5% decrease 2. 12.4% increase 3. 97.7% decrease 4. 108.5% increase 5. 24% increase 6. 9.4% increase 7. 60.7% decrease 8. 70% decrease 9. 30.8% increase 10. 19.7% increase 11. $10.76 12. $26,000.00