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8th Grade TAKS Review 2008

Objective 2

Day 1

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Rates• Rates can be expressed as:

• Speed (miles per hour)• Cost (Price per pound)• Cost per Item

• To determine the rate:

•Divide• Example: 100 miles in 2 hours

100 ÷ 2

50 miles per hour

Obj. 2: 8.3A

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Comparing Rates• Example: Store #1 sells a 12 ounce soda

for $1.29 and Store #2 sells a 16 ounce soda for $1.80. Which store has the best deal?

Obj. 2: 8.3A

Determine the rate for each store (cost per ounce)Store #1 Store #1$1.29 ÷ 12 = $1.80 ÷ 16 = $0.1075 per ounce $0.1125 per ounce

This is the best deal because it is the lowest cost per ounce!

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Comparing Rates, cont…• Example: A pet store sells an 8-pound bag

of dog food for $6.48. Which of the following represents the same price per pound?

A. A 20-pound bag for $24.69

B. A 15-pound bag for $12.15

C. A 10-pound bag for $8.48

D. A 5-pound bag for $3.48

Price per pound:

$6.48 ÷ 8 = $0.81

$24.69 ÷ 20 = $1.2345

$12.15 ÷ 15 = $0.81

$8.48 ÷ 10 = $0.848

$3.48 ÷ 5 = $0.696

Obj. 2: 8.3A

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Sales Tax• Sales tax is always added to the original

price of the item

• To find the sales tax multiply the tax rate by the original price

• Example: If a pair of shoes cost $19.99 and the tax rate is 8.5%, what is the total cost of the shoes?

Obj. 2: 8.3B

Original Price + Tax = Total Cost 19.99 + .085(19.99) = Total Cost 19.99 + 1.69915 = Total Cost $21.69 = Total Cost

= 0.085

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Sales Tax, Cont…• Example: Carmen bought 3 books for

$51.57. If each book cost $15.99 before tax was added, what tax rate did she pay?

A. 1.2%

B. 3.6%

C. 8.5%

D. 7.5%

Obj. 2: 8.3B

Original Price + Tax = Total Cost3(15.99) + tax(original price) = 51.57

47.97 + tax(47.97) = 51.57-47.97 -47.97

tax(47.97) = 3.60 47.97 47.97 tax = 0.075

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Sales Tax, Cont…• Example: Carmen bought 3 books for $51.57. If

each book cost $15.99 before tax was added, what tax rate did she pay?

A. 1.2%

B. 3.6%

C. 8.5%

D. 7.5%

Obj. 2: 8.3B

47.97 + tax(47.97) = 51.57Try each answer!

47.97 + 0.012(47.97) = 51.57 47.97 + 0.57564 = 51.57

47.97 + 0.036(47.97) = 51.57 47.97 + 1.72692 = 51.57

47.97 + 0.085(47.97) = 51.57 47.97 + 4.07745 = 51.57

47.97 + 0.075(47.97) = 51.57 47.97 + 3.59775 = 51.57

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Discounts• Discounts are always subtracted from the

original price

• To find the discount multiply the rate by the original price

• Example: A pair of shoes are on sale for 30% off the regular price of $25. What is the sale price of the shoes?

Obj. 2: 8.3B

Original Price - Discount = Sale Price 25 - 0.30(25) = Sale Price 25 - 0.30(25) = Sale Price 25 - 7.5 = $17.50

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Discounts, Cont…• Example: Mike saved $16 on a jacket that

was on sale. If the sale price was 20% off the regular price, what was the regular price?

A. $90

B. $80

C. $70

D. $32

Original Price x Rate = DiscountOriginal Price x 0.20 = 16

Try each answer!

90 x 0.20 =

80 x 0.20 =

70 x 0.20 =

32 x 0.20 =

18

16

14

6.4

Obj. 2: 8.3B

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Equations, Tables, and Graphs• Equations, Tables and Graphs are different

ways to represent the same data

• Example:

Equation Table Graph

Obj. 2: 8.4A

y = 2x + 3 X Y

-1

0

2

3

y = 2(-1) + 3 = 1 1

y = 2(0) + 3 = 3 3

y = 2(2) + 3 = 7 7

y = 2(3) + 3 = 9 9

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Equations, Tables, and Graphs, cont…

• Example: The table below shows a relationship between x and y. Which equation best represents this relationship?

Obj. 2: 8.4A

X Y

0 4

1 6

2 8

3 10

A. y = 4xB. y = x + 4C. y = 4x + 2D. y = 2x + 4

Try the first point.4 = 4(0)

4 = 0 + 44 = 4(0) + 24 = 2(0) + 4

Try the second point.

6 = 1 + 4

6 = 2(1) + 4

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Vocabulary• Rate – a comparison of numbers

• Speed – Distance ÷ Time

• Cost – amount needed to purchase an item

• Sales Tax – additional cost to purchase an item

• Discount – amount taken away from the cost of a purchase

• Equation – any expression with an “= sign”

• Table – a way to organize data

• Graph – a picture of dataX Y

-1

0

2

3