Percents

A survey asked students whether they had after-school jobs. Write each ratio as a fraction in simplest form.

Ratios and Unit Rates

a. all students surveyed to studentswithout jobs

b. all students surveyed to studentswith jobs

all students surveyedstudents with jobs

10040

=

= 52

After-School Jobs

Response Number

Have a Job 40

60

100

Don’t Have a Job

Total

all students surveyedstudents without jobs

10060

=

= 53

The table shows prices for different packages of index cards. Which size has the lowest unit price?


Price$2.70

$1.30$.75

100

5025

Size(cards)

100 cards: pricenumber of cards

$2.70100 cards

= $.027/card


$0.7525 cards

= $.03/card

The 50-card pack has the lowest unit price.


$1.3050 cards

= $.026/card Find the unit prices.

Convert 30 gal/min to cups/second.


30 gal/min = • •30 gal1 min

16 c1 gal

1 min60 s

Use conversion factors that convert gallons to cups and minutes to seconds.

1 min

1260 sDivide the common factors and units.

= • •130 gal1 min

816 c1 gal

= 8 cs

Simplify.

30 gal/min equals 8 c/s.

Solve = .

Proportions27

y14

Method 1: Multiplication Property of Equality

=27

y14

• 14 = • 1427

y14

= y287

4 = y

(continued)

ProportionsMethod 2: Cross products

=27

y14

2 • 14 = 7 • y

28 = 7y

4 = y

=287

7y7

Do the ratios and form a proportion? Explain.

Proportions

105 = 105 Simplify.

Yes; the ratios do form a proportion. The cross products are equal.

35

2135

Test by writing as a proportion.35

2135

3 • 35 5 • 21 Write cross products.

One hundred rods is about 275 fathoms. About how many fathoms is 25 rods?

ProportionsLet d = distance in fathoms.

length in rodslength in fathoms

100275

= 25d

distance in rodsdistance in fathoms

100d = 275(25) Write cross products.

d = 68.75 Simplify.

d = Divide each side by 100.275(25)100

25 rods is about 68.75 fathoms.

Trapezoid ABCD ~ trapezoid EFGH. Find the value of k.

Similar Figures and Scale Drawings

Write a proportion for corresponding sides.6k

Side AB corresponds = Side CD corresponds to side EF. to side GH.

32

6 • 2 = k • 3 Write cross products.

= Divide each side by 3.6 • 23

3k3

4 = k Simplify.

A flagpole casts a shadow 5 ft long. At the same time, a yardstick casts a shadow 1.5 ft long. The triangle shown for the flagpole and its shadow is similar to the triangle shown for the yardstick and its shadow. How tall is the flagpole?


Corresponding sides of similar triangles are in proportion.

1.55

= 3x

1.5x = 5 • 3 Write cross products.

Divide each side by 1.5.

1.5x1.5

= 5 • 31.5

x = 10 Simplify.

The flagpole is 10 ft tall.

The scale of a map is 1 in. : 24 mi. About how far is it between two cities that are 3 in. apart on the map?


It is about 72 mi between the two cities.

map (in.)actual (mi.)

124

3d

map (in.)actual (mi.)

= Write a proportion.

1 • d = 24 • 3 Write cross products.

d = 72 Simplify.

Write each percent as a fraction or a mixed number.

Fractions, Decimals, and Percents

a. 30%

b. 175%

Write as a fraction with a denominator of 100.30100

Simplify.310

Write as a fraction with a denominator of 100.175100

1 Write as a mixed number.34

Simplify.74

Express 7.3% as a decimal.


= 0.073

7.3% = Write as a fraction with a denominator of 100.7.3100

= 007.3 Divide by moving the decimal point two places to the left. You may need to write one or more zeros.

Express 0.412 as a percent.


Method 1: Rewrite as a fraction.

= 41.2%

Method 2: Move the decimal point.

0.412 = 41.2%

0.412 = 4121,000

= 412 ÷ 101,000 ÷ 10

= 41.2100

Four out of seven members of the chess club are boys. What percent of the chess club members are boys?


0.5714 Divide the numerator by the denominator.

57.14% Write as a percent.

About 57% of the chess club members are boys.

Write a fraction.47

Find 23% of 158.

Proportions and Percents

23(158) = 100n Write cross products.

36.34 = n Simplify.

23% of 158 is 36.34.

= Write a proportion.23100

n158

= Divide each side by 100.23(158)100

100n100

What percent of 34 is 28? Round to the nearest tenth of a percent.


34n = 100(28) Write cross products.

n = 82.35... Simplify.

= Write a proportion.n100

2834


34n34

28 is approximately 82.4% of 34.

82.4 Round.

216 is 72% of what number?


72n = 100(216) Write cross products.

n = 300 Simplify.


72n72


216n

216 is 72% of 300.

A tile floor has 90 blue tiles, which is 15% of all the tiles in the floor. How many tiles are in the floor in all?


15x = 100(90) Write cross products.

x = 600 Simplify.

The floor has 600 tiles in all.

Check: Is the answer reasonable? The problem says the number of blue tiles is 15%. 10% of 600 is 60, so 5% of 600 is 30, and 15% is 60 + 30 = 90. The answer is reasonable.


90x


15x15

What is 35% of 84?

Percents and Equations

n = 0.35 • 84 Write an equation. Write the percent as a decimal.

n = 29.4 Simplify.

35% of 84 is 29.4.

What percent of 26 is 65?


n • 26 = 65 Write an equation.

n = 2.5 Simplify.

= 250% Change the decimal to a percent.

65 is 250% of 26.

= Divide each side by 26.26n26

6526

A car salesman makes a 6.5% commission on each car he sells. How much does he make on the sale of a car for $35,000?


c = 0.065 • 35,000

= 2,275

The salesman’s commission is $2,275.

Words amount of commission is 6.5% of$35,000

Let c = amount of commission.

Equation c = 0.065 • $35,000

During a telephone survey, 414 people, or 46% of those called, said that they were watching station RFGT at the time of the call. How many people were called?


0.46n = 414

n = 900

900 people were called.

=0.46n0.46

4140.46

Words 414 is 46% of people called

Let n = number of people called.

Equation 414 = 0.46 • n

Find the percent of increase from 8 to 9.6.

Percent of Changeamount of increase = 9.6 – 8 = 1.6

= 0.2 = 20%

The percent of increase from 8 to 9.6 is 20%.

percent of increase = amount of increaseoriginal amount

= 1.68

In a given year, Hillsboro had a total of 7.5 in. of rain by March 1 and a total of 22.5 in. by July 1. Find the percent of increase from 7.5 to 22.5.

Percent of Change

amount of increase = 22.5 – 7.5 = 15

= 2 = 200%

The percent of increase from March 1 to July 1 was 200%.

percent of increase = amount of increaseoriginal amount

= 157.5

Find the percent of decrease from 1,250 to 1,120.

Percent of Changeamount of decrease = 1,250 – 1,120 = 130

= 0.104 = 10.4%

percent of decrease = amount of decreaseoriginal amount

= 1301,250

A grocery store has a 20% markup on a can of soup. The can of soup costs the store $1.25. Find the markup.

Markup and Discount

markup = percent of markup • store’s cost

= 0.2 • 1.25

= 0.25 Simplify.

The markup is $.25.

A bookstore pays $4.50 for a novel. The percent of markup is 45%. Find the novel’s selling price.

Markup and Discount

0.45 • 4.50 = 2.03 Multiply to find the markup.

4.50 + 2.03 = 6.53 Store’s cost + markup = selling price.

The selling price is $6.53.

A camera that regularly sells for $210 is on sale for 30% off. Find the discount.

Markup and Discount

discount = percent of discount • regular price

= 0.30 • 210

= 63

The discount is $63.

Percents

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