Pre Algebra Chapter 6

Name:

Multiple Choice
Identify the choice that best completes the statement or answers the question.

Write the ratio as a fraction in simplest form.

30 : 48

24 to 20

6 out of 9

In the population of a particular country, the male-to-female ratio is 46 to 54. Write this ratio as a fraction in simplest form.

Marty has saved $72. He spent $8 on a video rental. Write a ratio as a fraction in simplest form to represent what portion of his savings he has left.

Grace and Jamal each bought notebooks for school. Grace bought 3 notebooks for $3.90 while Jamal bought 2 notebooks for $2.20. What was the unit price of each student’s notebooks?

a.	Grace: $3.90; Jamal: $2.20	c.	Grace: $1.10; Jamal: $1.30
b.	Grace: $1.30; Jamal: $1.10	d.	Grace: $3.00; Jamal: $2.00

Convert 2 qt/min to gallons per hour.

8 gal/h

120 gal/h

30 gal/h

3 gal/h

Convert 50 mi/h to feet per minute.

4,400 ft/min

3,000 ft/min

1,200 ft/min

6,636 ft/min

Grete Waitz won the New York Marathon nine times. The rate at which she ran during her last victory in 1988 was 26 miles in 148 minutes. To the nearest hundredth, what was the unit rate for her last race?

5.69 mi/min

0.18 mi/min

0.26 mi/min

0.73 mi/min

Solve the proportion.

10.

882

11.

12.

787.5

320.5

31.5

3.5

13.

One hundred nautical miles equals about 185 kilometers. To the nearest kilometer, how far in kilometers is 290 nautical miles?

537 km

157 km

185 km

53,650 km

14.

Write a proportion that can be used to find the cost of 10 notebooks if 3 notebooks cost $1.98.

a.		c.
b.		d.

15.

At the school store, 6 pencils sell for $.99. At this rate, what is the cost of 16 pencils?

$2.64

$3.79

$2.98

$1.65

16.

Carpet Masters charges $9.50 per square yard to clean a carpet. If you have two rooms with an area of six square yards each, how much will it cost to have the carpets cleaned?

$3.17

$114

$228

$342

17.

Parallelogram PARL

parallelogram WXYZ. Find the value of c.

18.

The triangles are similar. Find the value of a.

19.

A building 50 ft high casts a 75-ft shadow. Sarah casts a 6-ft shadow. The triangle formed by the building and its shadow is similar to the triangle formed by Sarah and her shadow. How tall is Sarah?

4 ft

5 ft

3 ft

not here

20.

Gretchen is using an overhead projector to enlarge a drawing so she can make a poster. The original drawing measures 60 mm wide by 80 mm high. She moves the projector so that the width of the projected image is 300 mm. If the original drawing and the projected image are similar figures, what will be the height of the projected image?

440 mm

225 mm

180 mm

400 mm

21.

The scale on a map is 1 cm : 6 km. If two cities are 13 cm apart on the map, what is the actual distance between the cities?

13 km

468 km

2.17 km

78 km

22.

A map shows the distance between the corner of Cactus Road and 1st Street and the corner of 1st Street and Merle Road as 3 inches. If the scale is 1 in. : 3.7 mi, what is the actual distance?

1.3 mi

11.1 mi

111 mi

22.2 mi

23.

Find P(rolling 2 or 5) with one number cube.

24.

You have 15 pennies in your pocket. Of those pennies, 3 are Canadian. Suppose you pick a penny out of your pocket at random. Find P(not Canadian).

25.

You put the names of all the students in your class in a paper bag. There are 14 boys and 20 girls. If you draw a name at random, what is P(boy’s name)?

26.

A survey of teenagers found the music preferences listed. If you pick a teenager at random, what is P(rock)?

Country	Jazz	Rock	Classical	New Age	Other
12	5	7	6	6	4

27.

A bag contains 3 green marbles and 8 white marbles. Suppose a marble is randomly selected. What are the odds in favor of picking a white marble?

8 to 3

8 to 11

3 to 8

3 to 11

28.

A jar contains 45 red candies and 60 black candies. Suppose a candy is selected at random. What are the odds against selecting a red candy?

3 to 7

4 to 7

3 to 4

4 to 3

29.

The probability of winning a particular game at the Game Place is

. Find the odds against winning the game.

1 to 4

3 to 4

3 to 1

5 to 1

30.

Find 78% of 380. Round to the nearest tenth of a percent if necessary.

3.8

29,640.0

296.4

487.2

31.

What percent of 67 is 33? If necessary, round to the nearest tenth of a percent.

203.0%

0.5%

49.3%

33.0%

32.

Emma already has read 6 of 20 books on her summer reading list. What percent of the books on her list has she read already?

23.1%

30.0%

333.3%

0.3%

33.

Two U.S. states are not part of the continental United States. What percent of the fifty U.S. states are included in the continental United States?

13%

48%

96%

34.

20 is 50% of what number? If necessary, round to the nearest tenth.

10.0

1000.0

40.0

0.4

35.

The Mogul Runners ski club planned a trip to Park City. Of the total number of members belonging, 11 signed up to go. If this is 25% of the club, how many total members does the ski club have?

22 members

3 members

275 members

44 members

36.

Martha paid $42.40 for her sister’s birthday present. This included 6% sales tax. What was the cost of the gift before tax?

$40.00

$44.94

$25.44

$2.40

Write the percent as a fraction or mixed number in simplest form.

37.

35%

38.

155%

39.

Write 88.2% as a decimal.

8.82

882

0.882

8,820

40.

At the Mega Theater, 80% of the movies this weekend are comedies. As a fraction in simplest form, what fraction of the movies are comedies?

not here

Write the decimal as a percent.

41.

0.798

0.0798%

79.8%

7.98%

798%

42.

1.513

151.3%

1,513%

0.1513%

15.13%

Write the fraction as a percent. Round to the nearest tenth of a percent if necessary.

43.

0.425%

4.25%

42.5%

235.3%

44.

14.3%

1.43%

Write an equation and solve. Round to the nearest tenth where necessary.

45.

What is 35% of 63?

a.	; 180	c.	; 2,205
b.	; 22.05	d.	; 22.05

46.

19 is what percent of 40?

a.	; 47.5%	c.	; 40.4%
b.	; 2.1%	d.	; 52.3%

47.

64 is 80% of what?

a.	; 0.8	c.	; 80
b.	; 125	d.	; 1.3

48.

What percent of 24 is 30?

a.	n 24 = 30; 125%	c.	n = 30 24; 720%
b.	n 30 = 24; 80%	d.	n = 30 0.24; 720%

49.

21 is 35% of what number?

a.	; 62.4	c.	; 40.8
b.	; 7.4	d.	; 60

50.

Tamika makes a 5.5% commission selling electronics. How much commission does she make if she sells a flat-screen TV for $10,000?

$9,450

$550

$55,000

$1,818.18

51.

In a survey, 480 people, or 75%, said they attended a movie at least once a month. How many people were surveyed?

405 people

360 people

555 people

640 people

52.

Find the percent of increase from 320 to 380. Round to the nearest tenth of a percent if necessary.

18.8%

84.2%

15.8%

0.2%

53.

The sales of a particular brand of children’s athletic shoes rose from $6,900,000 to $7,400,000. Find the percent of increase in sales. Round to the nearest tenth of a percent if necessary.

6.8%

0.1%

93.2%

7.2%

54.

Find the percent of decrease from 280 to 210. Round to the nearest tenth of a percent if necessary.

25%

0.3%

33.3%

133.3%

55.

The circulation of a newsletter decreased from 3,200 to 2,464. What was the percent of decrease in circulation?

129%

77%

2.3%

23%

56.

Wren bought a baseball card last year for $2.25. This year the price dropped to $.45. What was the percent of decrease in the price of the card?

80%

500%

120%

400%

57.

A toy store’s percent of markup is 35%. A model train costs the store $100. Find the markup.

$135

$35

$285.71

$65

58.

A sporting goods store pays $180 for a rubber raft. The percent of markup is 40%. Find the raft’s selling price.

$72

$108

$252

$450

59.

All swimming equipment is on sale with a 35% discount. A snorkeling set regularly sells for $60. Find the discount.

$44.44

$39

$81

$21

60.

Video games are on sale for 35% off. If a particular game regularly sells for $99.50, what is the sale price?

$34.83

$96.02

$64.68

$134.33

61.

At the beginning of 1995, the town of Canyon Ridge had 1,700 residents. The rate of population growth after that was 6% per year. Estimate the population at the beginning of 2005.

a.	about 102 residents	c.	about 3,502 residents
b.	about 3,044 residents	d.	about 1,802 residents

62.

Soren placed $750 in a certificate of deposit (CD) with an interest rate of 3.5%. At the end of each year, the CD earns interest on the total amount including interest earned in previous years. How much money will there be after 5 interest payments?

$131.25

$881.25

$1,312.50

$890.76

63.

Cell phones are becoming very popular at Poplar Middle School. In 2000, there were 15 students with cell phones. Each year the number of students with cell phones has increased by 20%. At this rate, how many students will have cell phones in 2007?

44 students

54 students

35 students

38 students

64.

At Ron’s Roller Rink, the number of customers has been decreasing at a steady rate of 5% per year. If there were 900 skaters per week in 2000, what is a good estimate for the number of skaters per week in 2006?

778 skaters

662 skaters

695 skaters

732 skaters

Short Answer

Tell whether the two ratios form a proportion. Explain.

65.

and

66.

and

67.

The Student Council attended a convention. For lunch, 12 out of the 29 members chose milk to drink.
a. To the nearest tenth of a percent, what percent of the students chose milk?
b. To the nearest tenth of a percent, what percent of the students chose another beverage?

68.

Amy has a garden covering 900 square feet.

a. If she wants to plant moss roses on 10% of the garden, how many square feet will moss roses cover? Write and solve a percent equation to solve this problem.
b. If the garden occupies 25% of Amy’s yard, what is the area of her yard in square feet? Write and solve a percent equation to solve this problem.

69.

Ginnie bought a table cloth for $23.25. She embroidered a design on the table cloth and then sold it for $41.75.

a. What was the percent of increase in price of the tablecloth?
b. Suppose Ginnie wanted to make a profit of $24.50 on the sale of the tablecloth. What would be the percent of increase in the price for that amount of profit?

70.

Danielle manages a clothing store. For a special promotion, she receives a shipment of coats that cost her $85 each.

a. Usually, the percent of markup for her store is 70%. Find the usual selling price of one of the coats.
b. The owner of the store suggests that she mark each coat with a price tag of $127.5. What is the percent of markup for each coat?

71.

Suppose the cost of an item is c. First, the cost is discounted by 30%. Then sales tax of 6.5% is added to the sales price. Write an algebraic expression for the final cost of the item using the variable c.

72.

An engineer is drawing plans for a new water tower. The tower is 82 feet tall and the tank is circular with a diameter of 26 feet.

a. The engineer builds a model of the tower with a scale of 1 inch : 5 feet. What are the dimensions of the model?
b. Suppose the engineer decides to build a second model such that the height of model is 20 inches. What is the scale for the model?

73.

When a new model of computers became available, Computer World reduces the price of the older computers by 25%. Jeremy has $1,457 saved. If the original price of the computer is $2,000, does Jeremy have enough money to buy the computer at the sale price?

Essay

74.

Dane designed two gardens for a museum. The gardens are shaped as similar trapezoids as shown. Find the perimeter of the smaller garden. Show your work.

75.

Allen makes a 3.4% commission selling vehicles at a car dealership.
a. How much commission does he make on the sale of a $17,000 car? Show your work.

b. During one busy month, Allen’s total commission was $9,860. If a salesperson sells more than $200,000 in one month, the person receives a bonus. Did Allen receive a bonus? Explain.

76.

Susan drove to visit her cousin, driving a distance of 646 miles. The trip took 16 hours of driving time.
a. What was her average speed for the hours that she drove?

b. Susan wants to shorten her driving time by one half hour. What average speed should she drive to do this? Write and solve a proportion to find Susan’s new speed.

77.

Dorothy is a scientist studying the rate of growth of a particular type of bacteria. For an experiment, she begins with 37 bacteria on a slide. She finds that the number of bacteria on the slide doubles every 30 minutes.

a. Make a table showing the total number of bacteria at the end of every 30-minute period for 4 hours.
b. What is the percent of increase in the population of the bacteria on the slide from the beginning of the experiment to the end of 4 hours? Show your work.

Other

78.

In Mr. Hansen’s science class, 11 out of 29 students are going on the weekend field trip. In Ms. Chapman’s science class, 23 out of 33 students are going on the trip. Is the ratio of students attending the field trip in Mr. Hansen’s class the same as the ratio of students attending in Ms. Chapman’s class? Explain your method for finding the answer.

79.

New Look Jewelry is advertising that all jewelry will be on sale for 85% of regular price. Jewels of Joy is advertising that all jewelry will be discounted 20%. Which store has the better sale? Explain your reasoning.

80.

The table shows the results of a survey at Clark Fork School.

Do You Eat Breakfast Before School?
Always	Sometimes	Never
45	60	40

Your classmate sets up the proportion

to calculate the percent of students who never eat breakfast. Explain your classmate’s error.

81.

The Math Club operates a concession stand during special school events. One of their best-selling items is packaged fruit snacks. They buy cases of 36 individual bags of the snacks. Each case costs $9.00.

a. The percent markup for the snacks is 40%. What is the selling price of one individual bag of fruit snacks? Explain how you found the price.
b. During the holiday concert, the profit from the sale of the fruit snacks was $8.50. How many bags of fruit snacks did they sell? Explain how you found the number of bags sold.