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CC MATH I STANDARDS: UNIT 4

WARM UP: #1 - 5 : Convert the following decimals to percents or percents to decimals.

(1) 0.03

(2) 72.3%

(3) 0.6

(4) 1.58%

(5) 12%

(6) What number is 5% of 18?

(7) 8.3 is 40% of what number?

(8) Find 145% of 64.

Find Percents given values in the percent equation.

Step #1: Set Up Your Percent Equation

Step #2: DIVIDE your two values to solve for the decimal of the percent

Step #3: CONVERT the decimal to percent

1) What percent is 18 of 24?

2) 54 is what percent of 45?

3) What percent is 38.7 of 86?

OVERALL PERCENT v. PERCENT OF CHANGE

PERCENT OF CHANGE: Represents the change from the start to end values as a percent.

• PERCENT INCREASE: How much is Overall Percent is ABOVE 100%.

• PERCENT DECREASE: How much is Overall Percent is BELOW 100%.

#1a) What overall percent is 14 of 10?

b) What is the percent change of 14 of 10?

#2a) 60 is what overall percent of 80?

b) 60 is what percent of change for 80?

#3a) What is the overall percent of 60 to 54?

b) What is the percent change of 60 to 54?

#4a) What is the percent of 36 to 41.4?

b) What is the percent change of 36 to 41.4?

Calculate the Percent of Change:

Step #1: Divide the END value OVER the START Value (Based on percent equation)

Step #2: Find the percent of decimal form

Step #3: Find the difference from 100%

INCREASE = Above 100% AND DECREASE = Below 100%

Find the percent of change (increase or decrease) in each situation:

1) Start = 10

End = 12

2) Beginning = 50

End = 49

3) Original = 25

New = 29

4) Start = 60

End = 54

5) New = 36

Original = 50

6) End = 97.5

Start = 75

7) List Price = 45

Sale Price = 36

8) Before = 1200

After = 1284

9) Initial = 8

Final = 20

10) The old population was 75,300 and the current population is 87,348.

11) A new car cost $45,000 and was later sold as a used car for a price of $39,150.

CALCULATE VALUES with PERCENT OF CHANGE:

|PERCENT INCREASE: |PERCENT DECREASE: |

|STEP #1:ADD 100% AND Percent Increase |STEP #1: SUBTRACT 100% and Percent Decrease |

| | |

| |STEP #2: Convert Percent to decimal form |

|STEP #2: Convert Percent to decimal form |STEP #3: Solve Percent Equation |

|STEP #3: Solve Percent Equation |(START #) *(% DECIMAL) = (END #) |

|(START #)*(% DECIMAL) = (END #) |Key Terms: |

|Key Terms: |Sales, Discount, Depreciates, Decays |

|Tax, Appreciates, Grows, Interest | |

|PERCENT OF CHANGE |Percent Calculation |Decimal Form |Find END VALUE |

|10% | | |Initial = 120 |

|Increase | | | |

|25% | | |Original = 500 |

|Decrease | | | |

|9% | | |Original = 3000 |

|Decrease | | | |

|138% | | |Starting = 800 |

|Increase | | | |

|6.5% Appreciated | | |Starting = 2775 |

|13% Depreciated | | |Original = 900 |

|0.75% | | |Initial = 63 |

|Decay | | | |

|100% | | |Original = 295 |

|Growth | | | |

|47% | | |Original = 598 |

|Interest | | | |

|23% | | |Starting = 54 |

|Sale | | | |

CC MATH I STANDARDS: UNIT 4

PERCENT OF CHANGE:

|Identify the type of Percent of Change in the Problem based on key terms |

|PERCENT INCREASE: |PERCENT DECREASE: |

|Increase, Tax, Tip, Appreciates, Interest, Growth |Decrease, Sale, Discount, Depreciates, Decays, Loss |

|STEP #1: r = percent of change |STEP #1: r = percent of change |

|ADD: 100% + r% |SUBTRACT: 100% - r% |

|STEP #2: Convert Percent to DECIMAL FORM (Move decimal point LEFT two digits) |

|STEP #3: Use the Percent Equation to solve: (START #)*(%) = (END #) |

GRAPHIC ORGANIZER for Percent of Change Problems

|PERCENT OF CHANGE |PERCENT CALCULATION |Decimal Form |Find missing value |

| | | |(START #)*(%) = (END #) |

|15% Increase | | | |

|10% Decrease | | | |

|25% Sale | | | |

|20% Tip | | | |

|7.5% Interest | | | |

|32% Decay | | | |

|120% Growth | | | |

|20% Decrease | | | |

|5% Increase | | | |

|30% Increase | | | |

PERCENT OF CHANGE WORD PROBLEMS: Round Decimals to 2 Digits

• Identify if the problem is an increase or decrease case

SECTION 1: Calculate the END or FINAL Value

1) A concert tickets costs $45. The sales tax is 6.25%, what is the total price of the ticket?

2) A sweater is on sale for 35% off the original price. If the original price of the sweater is $38, what is the discounted price?

3) Mr. Smith went to BestBuy to buy a Playstation 3 for $400, but saw a sale of 25% off the original price, then how much would he pay?

4) Raquel is planning to go to prom and needs to buy a dress. She finds a designer dress that originally costs $500 but it’s 40% off. How much did Raquel pay for the dress?

5) Normally people say 20 percent is a good tip to give a waiter. If a meal cost you $23, what is the total bill after tip?

6) You planned to buy $96 on groceries, and brought coupons worth 5% off on your groceries. How much money did you end up spending at the grocery store?

7) The population grew 30% in one year. The population was 4500 in 1990. What is the population in 1991?

8) A savings account will allow you to earn 6.5% interest each year. If you started the year with $1370 in your account, how much total money is in your account after interest?

9) The number of bacteria in a petri dish is 40,000 cells. After one day of treatment, the number of bacteria decayed by 36%. How many bacteria cells are now in the dish?

10) The value of a car depreciated by 20% from when it was sold for $45,000. What is the car’s current value?

SECTION 2: Calculating the START or INITIAL Value:

1) If the final answer was number 93.6 with a 22% decrease, find the starting number.

2) Ralph Lauren is having a sale on all polo shirts for 17% off the list price. If the sale price is $33.20 for a polo, then what is the approximate list price one is sold for?

3) Tax was 8% and you paid $270 during your shopping spree. What is the original price of all of your items before tax was included?

4) After you had a really good waiter you decided to leave a 22% tip. If you ended up leaving $42.70 on the table, then how much was your food cost?

SECTION 3: ADVANCED EXAMPLES

1) Monica currently works for $12 per hour at her job. She is offered two options for her raise. She can either get bumped up to 13.50 per hour based OR she could take a 15% increase to her pay. Which option should Monica choose?

2) Target has coupons to use on the weekend. Coupon one is for $20 off your purchase and Coupon two is for 20% off your purchase. If Mr. Smith plans to get $90 worth of candy for class, which coupon should he bring to Target?

3) At Chili’s your party orders $120 worth of food. If you are first charged 7% tax on your food and afterwards pay a 20% tip to your waiter.

a. How much is your bill after tax?

b. How much is your total bill after tip is included?

4) Walmart lists an XBOX360 at $220. Walmart offered a 15% sale on all items in the store, and then you had a 10% off all electronics coupon.

a. How much is the XBOX after Walmart’s sale?

b. How much is the XBOX after the sale and then your coupon?

5) Burke Street Pizza is offering a 20% off sale on all large pizzas. Mikayla orders one large pizza for $18 before the sale. If she plans to include a 20% tip for delivery, then

a. How much is her pizza after the sale?

b. How much does she pay total after including tip?

6) A lunch entrée is $8.50 and tax is 6.5%. How much do you have to pay total for lunch and how much is just the tax amount?

7) A sale of 18% off is given for all items at a sporting goods store. If you plan to get $150 worth of list price items, then how much do you pay and how much is your savings?

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