Short Answer
|
|
|
In a survey, Eric, the team manager, asked the 120 soccer players in the
league which drink they preferred during and after the game.
| Drink | During Game | After Game | | Gatorade | 70 | 10 | | Ocean Spray | 10 | 80 | | Evian Water | 40 | 30 | | | |
|
|
|
1.
|
Write mathematical comparison statements about player drink preferences
during the game. a. One statement using
ratios
b. One statement using percents
|
|
|
2.
|
Write mathematical comparison statements about player drink preferences
after the game.
a. One statement using fractions
b. One statement
using differences
|
|
|
3.
|
a. Write a ratio to describe the number of
players who prefer Gatorade to Evian Water during the game.
b. Write an
equivalent form of the ratio.
|
|
|
4.
|
Ricardo, the soccer league director, made the following statements based on
Eric’s survey. Which statements are accurate? Explain how you made each decision. a. During the game, players prefer Ocean Spray to Evian Water by a
ratio of 4 to 1.
b. 25% of the players prefer Evian Water after the game.
c. More than half of the players prefer Gatorade during the
game.
|
|
|
5.
|
So far this year, the University of North Carolina Tar Heels have won 22 games
and lost 5 games. a. If they continue at the same pace and
lose 45 games, how many will they have won?
b. What is
an appropriate comparison to make between the number of games won and the number of games lost?
Explain your reasoning for the type of comparison you chose.
|
|
|
The school newspaper club votes to have a picnic for its 30 members. The
picnic planners investigate prices for food and drink at two stores and list their findings in a
table.
|
|
|
6.
|
How much does it cost to make 30 hamburger patties with ground beef purchased
from Streamline? Show your work.
|
|
|
7.
|
How much do 30 hamburger patties cost at Bulky’s? Show your work.
|
|
|
8.
|
Which store offers the better buy for cola? Explain.
|
|
|
9.
|
You need to purchase enough hamburger buns to make 30 sandwiches. Buns come in
packages of 8 or 12, depending where you shop. Where would you purchase the buns, and how much would
they cost? Explain.
|
|
|
10.
|
The meal at the picnic will include: · One 12-ounce can of cola
· One
hamburger with bun
· One small bag of potato chips (10.5 ounce
bag)
The school cafeteria donated mustard, ketchup, relish, onions, paper plates and
napkins. The students will buy each item at whichever store has the best price. There are 30
people attending the picnic. How much should the students charge each person in order to cover the
food expenses? Show how you determined the amount.
|
|
|
11.
|
Donuts4U has donuts on sale at 12 for $5.40. Use division to find
unit rates that answer the following questions: a. What is
the cost per donut?
b. How many donuts can you buy for a dollar?
|
|
|
12.
|
The school store sells pencils at 24 for $3.00. a. What are the two unit rates that she might compare?
b.
Compute each unit rate and tell what it means.
|
|
|
13.
|
Find a value of x that will make each proportion true.
|
|
|
Use the following data about Lincoln Middle School.
|
|
|
14.
|
How many girls are enrolled in Lincoln Middle School?
|
|
|
15.
|
Suppose there is one teacher on staff for every 25 students enrolled. Estimate
the number of teachers at Lincoln Middle School.
|
|
|
16.
|
Pentominoes Pizza introduced a new pizza called the Giant Foot to compete with
Wee Czar's 2-pizzas-for-the-price-of-1 offer. The Giant Foot is two 1-square-foot pizzas put
together. Pentominoes' ad claims that the Giant Foot is 25% larger than two Wee Czar's
12-inch round pizzas. A Giant Foot costs $8.99. Two 12-inch round pizzas from Wee Czar's cost
$8.88.
a. Which offer gives you more pizza for your money?
b. Is the Giant Foot 25 % larger than two 12-inch round pizzas from
Wee Czar's? If so, prove it. If not, use percents to show how they really compare.
|
|
|
17.
|
Which offer is the better buy? 2-liter bottles of Orange Splash! |  -liter bottles of Orange
Splash! | $1.99 per 8-pack | 4 for $4.99 | | |
|
|
|
18.
|
Leticia is shopping for gifts. She compared prices at two stores so she could
get the best deals. For each item, tell which store has the best price. 
|
|
|
Use the data below. The table shows the all-time top 10 American movies in
terms of earnings.
All-Time Top Ten American Movies | Rank | Title (Year released) | Earnings
(millions) | 1 | E. T. The Extra-Terrestrial
(1992) | $399.8 | 2 | Jurassic Park (1993) | 356.8 | 3 | Star
Wars (1977) | 322.0 | 4 | The
Lion King (1993) | 310.1 | 5 | Forest
Gump (1993) | 300.6 | 6 | Home
Alone (1990) | 285.5 | 7 | Return
of the Jedi (1983) | 263.0 | 8 | Jaws
(1975) | 260.0 | 9 | Batman
(1989) | 251.2 | 10 | Raiders of the Lost Ark (1984 | 242.4 | | | Total
Earnings | $2991.4 | | | |
Source: Variety, Feb.
20-26, 1995, as found in The World Almanac and Book of Facts 1996. Ed. Robert Famighetti.
Mahwah, New Jersey: Funk and Wagnalls, 1995, p. 250.
|
|
|
19.
|
How do the earnings of E.T. The Extra-Terrestrial and Raiders of the
Lost Ark compare?
|
|
|
20.
|
Write a fraction that compares the earnings between Forrest Gump to the
total earnings from the top 10 movies.
|
|
|
21.
|
Write a ratio that compares the earnings of Jurassic Park to
Batman.
|
|
|
22.
|
Write a decimal that compares the earnings of Star Wars to the total
earnings from the top 10 movies.
|
|
|
23.
|
Mr. Martinelli's science class wants to make a scale model of the universe
for the science fair. They need to make some calculations before building their model. a. The diameter of the Sun is 865,000 miles. If the class made the
Earth's diameter = 1 inch, what would be the diameter of the scale model of the
Sun?
b. If they made Earth's diameter = 1 inch, what would be the diameter of the
scale model of Jupiter?
c. If they made Earth's diameter = 1 inch, what would be the
diameter of the scale model of Pluto?
d. If the class placed the planets by using a scale
of 1 inch = 1 million miles, how many feet from the Sun would the model of Mercury have to be
placed?
e. Using the scale 1 inch = 1 million miles, how far from the Sun would the model
of Earth have to be placed?
f. Using the scale 1 inch = 1 million miles, how far from the
Sun would the model of Pluto have to be placed?
|
|
|
24.
|
The table below shows the number of years a typical person spends engaged in
various activities over a lifetime: a. According to the table, how long is
a typical person’s lifetime? Explain your
reasoning.
b.
Does a typical person spend more years watching TV or sleeping? Write a ratio that compares these two
amounts.
c. The number of years spent doing miscellaneous activities is about how many
times the number of years spent socializing?
d. What percent of the total number of years
in a lifetime, are spent sleeping? What percent are spent at work or school?
e. About what
fraction of a lifetime is spent watching TV and talking on the phone? What fraction is spent in
miscellaneous activities?
f. Make an interesting comparison statement about the data in the
table. Tell why you think your comparison is interesting.
|
|
|
25.
|
Of the 756 students in Chad’s middle school, 44% participate in sports,
29% play in the band, and 37% take the bus to school. a. How
many students in Chad’s middle school play in the band? Explain your reasoning.
b.
How many students in Chad’s middle school take the bus to school?
c. If you add up the percents of students who play sports, play in
the band, and take the bus to school, you get 110%. Explain why the percents do not add to
100%.
|
|
|
26.
|
Of the students in Ms. Yadav’s fourth-period math class, 16 are wearing
athletic shoes, 10 are wearing boots, and 4 are wearing other kinds of shoes. a. What fraction of Ms. Yadav’s students are wearing boots?
Explain your reasoning.
b. Suppose 1006 students attend
the middle school where Ms. Yadav teaches. Use your answer from part a to estimate the number of
students who are wearing boots. Explain your reasoning.
|
|
|
27.
|
Bill has a paper route in his neighborhood. It takes him 50 minutes to deliver
newspapers to the 40 customers on his route. a. How long will
it take Bill to complete his route if he adds 20 more customers in his neighborhood? Explain your
reasoning.
b. Only 30 of Bill’s 40 customers take the Sunday paper. About how long
does it take Bill to deliver his papers on Sundays?
|
|
|
28.
|
Betty and Derek are making punch for a class party. The directions on the liquid
punch mix say to use 3 cups of mix for every 7 cups of water. Betty and Derek want to make enough
punch so that each of the 25 people at the party can have 2 cups. a. How many cups of punch mix will Betty and Derek need to use?
Explain your reasoning.
b. How many cups of water will Betty and Derek need to
use?
c. Betty and Derek want to put the punch in bowls that hold 20 cups each. How many
bowls will they need?
|
|
|
29.
|
Brice found three recipes for blueberry syrup. Of the ingredients, the
ingredients only differed on the amount of blueberries and sugar: Classic Blueberry syrup: 6 cups blueberries and 2 cups sugar
Homestyle
Blueberry syrup: 2 cups blueberries and 1/2 cup sugar
Country Blueberry syrup: 20 cups blueberries
and 7 cups sugar
Which recipe will be the sweetest? Explain your reasoning.
|
|
|
30.
|
At Louis Armstrong School, Ms. Turini’s homeroom has 18 boys and 12 girls.
Use ratios to describe the gender distribution of this class, by answering the following questions in
at least two equivalent ways. a. What is the ratio of boys to
girls in Ms. Turini’s homeroom?
b. What is the ratio of girls to boys?
c.
What is the ratio of boys to students in the class?
d. What is the ratio of students in the class to boys?
|
|
|
31.
|
Josh jogs an average of 8 miles per week for three weeks.
a. At this rate, how many miles will he jog in 52
weeks?
b. How many miles will he need to jog during the
fourth week to bring his four-week average to 10 miles per week?
|
|
|
32.
|
Tony can type at a constant rate of 55 words per minutes.
a. Write an equation for the number of words, W, Tony can type
in T minutes.
b. How many words can Tony type in 20 minutes?
c. If Tony
has a half hour to type a 1,600-word essay, will he have time to type the entire essay? Explain your
reasoning.
|
|
|
33.
|
The following table shows caffeine content of 12-ounce cans for five popular
soft drinks. a. Complete entries in the column giving caffeine content of 20-ounce
bottles for each soft drink.
b. Complete the following sentences comparing caffeine content
in soft drinks. In each case, use the exact data first. Then give a simpler ratio that is exactly or
nearly equivalent to the first.
i. The ratio of
caffeine in Diet Sun Drop to that in Barq’s Root Beer is … or about …
ii.
The ratio of caffeine in Mountain Dew to that in Dr. Pepper is … or about
…
iii. The ratio of caffeine in Mountain Dew to that in Coca Cola is … or about
…
|
|
|
34.
|
When people predict the chances that some athlete, team, racehorse, or car will
win a competition, they often express their guess as a statement about the “odds against”
winning. For example, they might predict that odds on the Yankees winning the World Series are 7 to
2, meaning that the probability of that event is  . A horse that leaves the
starting gate with odds 11 to 5 is predicted to have probability  of
winning. a. What is the probability that a team will win a
game if the reported odds are 6 to 4? 8 to 5? 3 to 5? A to B? b. What simpler odds
statements could be given if the reported odds are 12 to 9? 8 to 2? 15 to 6? c. What odds
would be stated if the probability of winning a contest is  ?  ?
 ?  ?
|
|
|
35.
|
A veterinarian’s clinic has a patient load of 150 cats and dogs. The ratio
of cats to dogs is 4 to 8. How many patients are cats and how many are dogs? Explain your
reasoning.
|
|
|
36.
|
On a map, 1 centimeter = 50 kilometers. What is the actual distance between two
towns that are 3.5 centimeters apart on the map? Explain your reasoning.
|
|
|
37.
|
In a home-run derby contest after the little league baseball session had ended,
Calvin hit 4 homeruns out of his 12 hits. Suppose Calvin’s success rate stays about the same
for his next 100 hits. Write and solve proportions to answer these questions. a. About how many homeruns will Calvin make out of his next 48
hits?
b. About how many homeruns will Calvin make out of his next 84 hits?
c.
About how many hits will it take for Calvin to hit 8 more homeruns?
d. About how many hits will it take for him to make 36 more
homeruns?
|
|
|
38.
|
Find the value of x that makes the two ratios equivalent. | a. | 4 to 7 and x to
63 | b. | 4 to 7 and x to
87.15 | c. | 12 to x and 4 to
117 | | d. | 12 to
x and 15 to 45 | e. | 2 to 3 and
7 to x | f. | 23 to 115 and
x to 15 | | | | | | |
|
|
|
39.
|
The Elsie Dairy uses a machine that fills 28 cartons of milk an hour. a. How many cartons will be filled in 6.5 hours?
b. How
long will it take to fill 343 cartons?
c. If the machine ran continuously for 10 days, how
many cartons would it fill?
d. Write an equation that expresses the relationship between
the number of cartons, C, and the number of hours, H.
|
|
|
40.
|
A sign at the fair advertised ticket prices for the carnival games. a.
Find the unit price for each ticket color.
Red
Tickets
Blue Tickets
Yellow Tickets
b. How much would 40 red tickets cost?
c. How many blue
tickets could you buy for $20.00?
|
|
|
41.
|
The fair train ride covered a distance of 3 miles in 20 minutes. a. What was the speed for the ride in miles per minute?
b.
What is the speed for the ride in miles per hour?
c. Write an equation you can use to
determine how long it would take the train to cover any distance if it traveled at this same
speed.
d. How far would the train travel in 45 minutes?
|
|
|
42.
|
There are 64 pretzels in a 16-ounce bag of chocolate covered pretzels. a. Write and solve a proportion that you can use to find the number
of chocolate covered pretzels in a 5-ounce bag.
b. What is the number of chocolate covered
pretzels per ounce?
c. How many ounces does each
pretzel weigh?
|
|
|
43.
|
There are two doorways into the fun house. The doors are similar rectangles. The
tall door is 9 feet high and 5 feet wide. The short door is 4 feet high. How wide is the short
door?
|
Multiple Choice
Identify the
choice that best completes the statement or answers the question.
|
|
|
44.
|
The ratio of boys to girls in a class is 2 to 3. There are 12 boys in the class.
How many girls are there?
|
|
|
45.
|
One can of Mountain Dew costs $1.25 in a vending machine.
A 12-pack of
Mountain Dew costs $3.49 at the grocery store.
How much money would you save by purchasing a
dozen cans of Mountain Dew at the grocery store instead of a dozen at the vending machine?
a. | $2.24 | b. | $ 0.96 | c. | $11.51 | d. | $12.49 |
|
|
|
46.
|
Find the value of x in this proportion.
|
|
|
47.
|
The ratio of teachers to students is 1 to 26. Find an equivalent ratio.
a. | 52 to 2 | b. | 11 to 36 | c. | 26 to 1 | d. | 5 to
130 |
|
|
|
48.
|
The ratio of strawberries to raspberries in a fruit smoothie drink is 4 to 12.
What percent of the drink is strawberries?
|
|
|
49.
|
Which size Dairy Queen Blizzard gives you the best price per ounce?
Small 6 oz. cup for $2.49
Medium 10 oz. cup for $3.49
Large 16 oz.
cup for $4.99
Super Size 24 oz. cup for $7.69
a. | Small | b. | Medium | c. | Large | d. | Super
Size |
|
|
|
50.
|
Lorreen sells 18 adult tickets, 23 student tickets, and 10 discount tickets for
the school play. Write the ratio student tickets to adult tickets in three ways.
a. | 23:10,  , 23 to 10 | c. | 23:18,  , 23 to
18 | b. | 18:23,  , 10 to 18 | d. | 10:18,  , 10 to
18 |
|
|
|
Write a ratio for the situation in three ways, comparing the first quantity
to the second quantity.
|
|
|
51.
|
A zoo has 17 monkeys and 7 chimpanzees.
a. | 7 to 17, 7 : 17,  | b. | 7 to 24, 7 : 24,
 | c. | 17 to 7, 17 : 7,
 | d. | 17 to 24, 17 : 24,
 |
|
|
|
52.
|
Represent the ratio 6 : 18 in two other ways.
a. |  , 6 to 18 | c. |  , 18 to
6 | b. |  , 18 to 6 | d. |  , 6 to
18 |
|
|
|
53.
|
You pay $4.50 for 9 bagels. What is the unit price?
a. | $0.50 per bagel | c. | $0.56 per bagel | b. | $0.60 per bagel | d. | $0.41 per bagel |
|
|
|
54.
|
Which is the best buy?
a. | $24.24 for 12 bottles of juice | c. | $16.32 for 8 bottles of
juice | b. | $18.09 for 9 bottles of juice | d. | $22.33 for 11 bottles of
juice |
|
|
|
55.
|
A store sells packages of pencils. Which package offers the best unit
price?
a. | 11 pencils for $2.97 | c. | 14 pencils for $3.64 | b. | 12 pencils for $2.88 | d. | 15 pencils for
$3.75 |
|
|
|
Compare. Use <, >, or =.
|
|
|
56.
|
|
|
|
Express the ratio as a decimal. Round to the nearest hundredth.
|
|
|
57.
|
2 : 10
|
|
|
58.
|
|
|
|
59.
|
Write  in simplest form.
|
|
|
60.
|
Jake sold 42 tickets to the school fair and Jeanne sold 9 tickets. What is the
ratio, in simplest form, of the number of tickets Jeanne sold to the number of tickets Jake
sold?
|
|
|
Write the ratio in simplest form.
|
|
|
61.
|
|
|
|
62.
|
32 min : 36 min
a. | 8 : 9 | b. | 8 : 36 | c. | 32 : 9 | d. | 128 :
144 |
|
|
|
63.
|
Marie saved $51. On Wednesday, she spent $8 of her savings. What ratio
represents the portion of her total savings that she still has left?
a. | 43 : 8 | b. | 8 : 51 | c. | 43 : 51 | d. | 59 :
51 |
|
|
|
64.
|
Write two different ratios equal to 6 : 30.
|
|
|
Find the value that completes the proportion.
|
|
|
65.
|
|
|
|
66.
|
|
|
|
67.
|
A car travels 136 miles using 7 gallons of gas. At that rate, how far can the
car travel using 42 gallons of gas?
a. | 1,224 mi | b. | 816 mi | c. | 952 mi | d. | 1,088
mi |
|
|
|
68.
|
Write three ratios equal to  .
|
|
|
Find a ratio equal to the ratio given.
|
|
|
69.
|
6 : 7
a. | 14 : 12 | b. | 6 : 14 | c. | 12 : 28 | d. | 12 :
14 |
|
|
|
70.
|
44 : 33
a. | 3 : 4 | b. | 40 : 3 | c. | 4 : 3 | d. | 4 :
27 |
|
|
|
Find the unit rate for the situation.
|
|
|
71.
|
336 km in 8 h
a. | 84 km/h | b. | 44 km/h | c. | 42 km/h | d. | 43
km/h |
|
|
|
Write a unit rate for the situation. Round to the nearest hundredth if
necessary.
|
|
|
72.
|
traveling 209 km in 5 h
a. | 41.8 km/h | b. | 0.02 km/h | c. | 52.25 km/h | d. | 34.83
km/h |
|
|
|
73.
|
A soccer player scored 41 goals in 84 games. Express the player’s scoring
rate as a unit rate rounded to the nearest thousandth.
a. | 0.4881 goals per game | c. | 0.488 goals per game | b. | 2.049 goals per game | d. | 2.0488 goals per
game |
|
|
|
74.
|
The price of 8.4 ounces of crackers is $2.42. What is the unit price? Round your
answer to the nearest cent.
a. | $0.15 per ounce | c. | $28.81 per ounce | b. | $3.47 per ounce | d. | $0.29 per ounce |
|
|
|
75.
|
Jonah needs to purchase 30 juice packs for his class. While shopping, Jonah
discovers the following prices for comparable juice packs. Which offers the best unit price?
a. | 15 packs for $3.95 | c. | 20 packs for $6.20 | b. | 5 packs for $2.20 | d. | 10 packs for
$3.20 |
|
|
|
Solve the proportion.
|
|
|
76.
|
|
|
|
77.
|
|
|
|
78.
|
|
|
|
79.
|
A van travels 180 miles on 6 gallons of gas. How many gallons will it need to
travel 750 miles?
a. | 75 gallons | b. | 25 gallons | c. | 50 gallons | d. | 225
gallons |
|
|
|
The triangles below are similar. Find the value of x.
|
|
|
80.
|
|
|
|
81.
|
|
|
|
82.
|
A 6-ft adult has a shadow 3.6 ft long. How long is the shadow of a 5-ft child
standing next to the adult?  a. | 3.6 ft | b. | 2.6 ft | c. | 4 ft | d. | 3
ft |
|
|
|
83.
|
The ladders shown below are standing against the wall at the same angle. How
high up the wall does the longer ladder go? (All measurements are in feet.)  a. | 26 ft | b. | 14 ft | c. | 12.5 ft | d. | 11.25
ft |
|
|
|
84.
|
Refer to the diagram below. Surveyors know that  and  are similar. What is PQ, the distance across the lake?  a. | 3.65 km | b. | 3.29 km | c. | 2.89 km | d. | 3.15
km |
|
|
|
85.
|
A dozen apples costs $2.55. At this rate, how much would 8 apples cost?
a. | $20.40 | b. | $3.83 | c. | $0.21 | d. | $1.70 |
|
|
|
Solve the proportion.
|
|
|
86.
|
|
|
|
87.
|
Parallelogram PARL  parallelogram WXYZ.
Find the value of c. 
|
|
|
88.
|
One hundred nautical miles equals about 185 kilometers. To the nearest
kilometer, how far in kilometers is 290 nautical miles?
a. | 537 km | b. | 157 km | c. | 185 km | d. | 53,650
km |
|
|
|
89.
|
Drinking 6 fluid ounces of milk provides 202.5 milligrams of calcium. How many
fluid ounces of milk provide 85.5 milligrams of calcium? Round to the nearest tenth.
a. | 3.0 fluid ounces | c. | 2.2 fluid ounces | b. | 2.5 fluid ounces | d. | 2.7 fluid
ounces |
|
|
|
90.
|
A machine takes 2.8 hours to make 9 parts. At that rate, how many parts can the
machine make in 28.0 hours?
a. | 226 parts | b. | 90 parts | c. | 81 parts | d. | 8
parts |
|
|
|
91.
|
Apples cost $3.60 for 2 lb. At that rate, how many pounds of apples can you buy
for $5.40?
|
|
|
92.
|
An astronaut who weighs 126 lb on Earth weighs only 21 lb on the moon. How much
would a person who weighs 25 lb on the moon weigh on Earth?
a. | 162 lb | b. | 150 lb | c. | 130 lb | d. | 105
lb |
|
|
|
93.
|
Sarah’s mother has a miniature village modeled after her home town. The
model is 10 feet long and 7 feet wide. The actual village is 7 miles long. What is the
village’s actual width? If necessary, round to the nearest tenth of a mile.
a. | 4.9 miles | b. | 10 miles | c. | 1 miles | d. | 0.7
miles |
|