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8-9 Percent Problems

6th Grade Math HOMEWORK

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ANSWERS!

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8-10 Using Percents

6th Grade Math HOMEWORK

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Our Learning Goal for Chapter 8Students will understand ratios, proportions, and percents by being able to write ratios, find unit rates, solve proportions, identify similar figures, find unknown measures, make scale drawings, understand relationships, and solve problems including those involving discounts, tips, sales tax, and simple interest.

Our Learning Goal Assignments• Learn to write ratios and rates and to find unit rates (8-1)• Learn to write and solve proportions (8-2)• Learn to use proportions to make conversions within the

customary system (8-3)• Learn to use ratios to identify similar figures (8-4)• Learn to use proportions and similar figures to find unknown

measures (8-5)• Learn to read and use map scale and scale drawings (8-6)• Learn to write percents as decimals and as fractions (8-7)• Learn to write decimals and fractions as percents (8-8)• Learn to find the missing value in a percent problem (8-9)• Learn to solve percent problems that involve discounts, tips,

and sales tax (8-10)

8-10 Using Percents

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpFind the percent of each number.

1. 75% of 300

2. 93% of 56

3. 32% of 128

4. 9% of 60

225

52.08

40.96

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8-10 Using Percents

5.4

Problem of the Day

A chessboard is 8 squares wide by 8 squares long. Each player has 8 pawns, 1 king, and 7 other pieces. At the start of a game, all the pieces are on the board, 1 piece per square. What percent of the total number of squares have a chess piece?

50%

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8-10 Using Percents

Today’s Learning Goal Assignment

Learn to solve percent problems that involve discounts, tips, and sales tax. Course 1

8-10 Using Percents

Vocabulary

discounttipsales tax

Insert Lesson Title Here

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8-10 Using Percents

Common Uses of Percents

Discounts A discount is an amount that is subtracted from the regular price of an item. discount = price • discount rate total cost = price – discount

Tips A tip is an amount added to a bill for service. tip = bill • tip rate total cost = bill + tip

Sales tax Sales tax is an amount added to the price of an item.

sales tax = price • sales tax rate total cost = price + sales tax

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8-10 Using Percents

Additional Example 1: Finding Discounts A clothing store is having a 10% off sale. If Angela wants to buy a sweater whose regular price is $19.95, about how much will she pay for the sweater after the discount?

Step 1: First round $19.95 to $20.

Step 2: Find 10% of $20 by multiplying 0.10 • 20. (Hint: Moving the decimal point one place left is a shortcut.)

10% of 20 = 0.10 • $20 = $2.00

The approximate discount is $2.00. Subtract this amount from $20.00 to estimate the cost of the sweater. $20.00 – $2.00 = $18.00

Angela will pay about $18.00 for the sweater.Course 1

8-10 Using Percents

To multiply by 0.10, move the decimal point one place left.

Remember!

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8-10 Using Percents

Try This: Example 1 A fishing store is having a 10% off sale. If Gerald wants to buy a fishing pole whose regular price is $39.95, about how much will he pay for the pole after the discount?

Step 1: First round $39.95 to $40.

Step 2: Find 10% of $40 by multiplying 0.10 • 40.

10% of 40 = 0.10 • $40 = $4.00

The approximate discount is $4.00. Subtract this amount from $40.00 to estimate the cost of the pole. $40.00 - $4.00 = $36.00

Gerald will pay about $36.00 for the fishing pole.

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8-10 Using Percents

When estimating percents, use percents that you can calculate mentally.

• You can find 10% of a number by moving the decimal point one place to the left.

• You can find 1% of a number by moving the decimal point two places to the left.

• You can find 5% of a number by finding one-half of 10% of the number.

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8-10 Using Percents

Additional Example 2: Finding Tips

Ben’s dinner bill is $7.85. He wants to leave a tip that is 15% of the bill. About how much should his tip be?Step 1: First round $7.85 to $8.

Step 2: Think: 15% = 10% + 5%

Step 3: 5% = 10% ÷ 2

= $0.80 ÷ 2 = $0.40Step 4: 15% = 10% + 5%.

Ben should leave about $1.20 as a tip.

= $0.80 + $0.40 = $1.20

10% of $8 = 0.10 • $8 = $0.80

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8-10 Using Percents

Try This: Example 2

Lita’s dinner bill is $11.95. She wants to leave a tip that is 15% of the bill. About how much should her tip be?Step 1: First round $11.95 to $12.

Step 2: Think: 15% = 10% + 5%

Step 3: 5% = 10% ÷ 2

= $1.20 ÷ 2 = $0.60Step 4: 15% = 10% + 5%.

Lita should leave about $1.80 as a tip.

= $1.20 + $0.60 = $1.80

10% of $12 = 0.10 • $12 = $1.20

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8-10 Using Percents

Additional Example 3: Finding Sales Tax Ann is buying a dog bed for $29.75. The sales tax rate is 7%. About how much will the total cost of the dog bed be?Step 1: First round $29.75 to $30.

Step 2: Think: 7% = 7 • 1%1% of $30 = 0.01 • $30 = $0.30

Step 3: 7% = 7 • 1%.

= 7 • $0.30 = $2.10.

The approximate sales tax is $2.10. Add this amount to $30 to estimate the total cost of the dog bed.

$30 + $2.10 = $32.10

Ann will pay about $32.10 for the dog bed.

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8-10 Using Percents

Try This: Example 3 Erik is buying a blanket for $19.83. The sales tax rate is 8%. About how much will the total cost of the blanket be?Step 1: First round $19.83 to $20.

Step 2: Think: 8% = 8 • 1%1% of $20 = 0.01 • $20 = $0.20

Step 3: 8% = 8 • 1%

= 8 • $0.20 = $1.60.

The approximate sales tax is $1.60. Add this amount to $20 to estimate the total cost of the blanket.

$20 + $1.60 = $21.60

Erik will pay about $21.60 for the blanket.

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Lesson Quiz

1. Sean’s new jeans are priced at $29.97, but the sale sign reads, “Take 15% off.” About how much will the jeans cost after the discount?

2. The bill for a family dinner comes to $56.78. About how much would a 20% tip be?

3. The price on a book is $12.99. If sales tax is 4%, about how much will its total cost be?

4. Megan wants a new bike. She is happy to see a sign that reads, “All bikes 10% off.” If the original price of the bike was $159.90 and sales tax is 6%, about how much will the total cost of the bike be?

About $11.50

About $25.50

Insert Lesson Title Here

About $13.50

About $150Course 1

8-10 Using Percents