Question: Diana bought a bag of colored chocolate candies. Before putting them into a bowl, she counted the number of candies of each color in a frequency chart. Diana then puts another bag of 56 black and white chocolate candies into a second bowl. How many candies are in both bowls combined?

Answer: 114

Color | Frequency
red | 7
orange | 12
yellow | 8
green | 11
blue | 13
brown | 7

Solution:
Step 1: Find how many candies are in the first bowl.
Add all of the frequencies.
7 + 12 + 8 + 11 + 13 + 7 = 58
So, there are 58 candies in the first bowl.
Step 2: Find how many candies are in both bowls combined.
Add the number of candies in the first bowl and the number in the second bowl.
58 + 56 = 114
So, there are 114 candies in both bowls combined.


Question: How much more does an Australian vacation package cost than a Jamaican vacation package?

Answer: 2,625

European vacation package | $7,668
African safari vacation package | $4,813
Jamaican vacation package | $7,039
Australian vacation package | $9,664
Hawaiian vacation package | $4,383

European vacation package
African safari vacation package
Jamaican vacation package
Australian vacation package
Hawaiian vacation package

Solution:
Subtract the price of a Jamaican vacation package from the price of an Australian vacation package.

$9,664 - $7,039 = $2,625

An Australian vacation package costs $2,625 more than a Jamaican vacation package.


Question: A bookstore employee looked up how many books were sold each month. In which month did the bookstore sell the fewest books?

Choices:
- April
- May
- June
- July

Answer: June

Month | Number of books
April | 797
May | 796
June | 769
July | 776

Solution:
Find the least number in the table. Remember to compare the numbers starting with the highest place value. The least number is 769.

Now find the corresponding month. June corresponds to 769.


Question: Gwen wants to buy 3 pounds of tapioca pudding. How much will she spend?

Answer: 13.26

chocolate pudding | $3.05/pound
rice pudding | $4.68/pound
tapioca pudding | $4.42/pound
vanilla pudding | $6.92/pound
butterscotch pudding | $2.68/pound

chocolate pudding
rice pudding
tapioca pudding
vanilla pudding
butterscotch pudding

Solution:
Find the cost of the tapioca pudding. Multiply the price per pound by the number of pounds.

$4.42 × 3 = $13.26

She will spend $13.26.


Question: Each restaurant table has 2 salt shakers. How many salt shakers are on 3 restaurant tables?

Answer: 6

Number of restaurant tables | Number of salt shakers
1 | 2
2 | 4
3 | ?

Solution: Count by twos. Use the chart: there are 6 salt shakers on 3 restaurant tables.


Question: Each shelf has 5 belts. How many belts are on 3 shelves?

Answer: 15

Number of shelves | Number of belts
1 | 5
2 | 10
3 | ?

Solution: Count by fives. Use the chart: there are 15 belts on 3 shelves.


Question: In science class, Trisha is measuring the temperature of different chemical mixtures. The temperatures of two mixtures are shown in the table. Which mixture's temperature is closest to zero?

Choices:
- bromine mixture
- acetone mixture

Answer: bromine mixture

Mixture | Temperature (°C)
Bromine mixture | -4
Acetone mixture | 5

Solution:
A positive number means the temperature is above zero. A negative number means the temperature is below zero.
To find the temperature closest to zero, use absolute value. The absolute value of a temperature tells you how far it is from zero.
Bromine mixture: |-4| = 4
Acetone mixture: |5| = 5
The temperature of the bromine mixture is closest to zero. It is only 4 degrees below zero.


Question: Edna, a soup chef at a new restaurant, kept track of the first week's soup sales. What is the probability that a randomly selected soup was ordered in a cup and was split pea? Simplify any fractions.

Answer: 3/17

 | Split pea | Chicken noodle
Cup | 3 | 6
Bowl | 5 | 3

Solution:
Let A be the event "the soup was ordered in a cup" and B be the event "the soup was split pea".
To find the probability that a soup was ordered in a cup and was split pea, first identify the sample space and the event.
The outcomes in the sample space are the different soups. Each soup is equally likely to be selected, so this is a uniform probability model.
The event is A and B, "the soup was ordered in a cup and was split pea".
Since this is a uniform probability model, count the number of outcomes in the event A and B and count the total number of outcomes. Then, divide them to compute the probability.

Find the number of outcomes in the event A and B.
A and B is the event "the soup was ordered in a cup and was split pea", so look at the table to see how many soups were ordered in a cup and were split pea.
The number of soups that were ordered in a cup and were split pea is 3.

Find the total number of outcomes.
Add all the numbers in the table to find the total number of soups.
3 + 5 + 6 + 3 = 17

Find P(A and B).
Since all outcomes are equally likely, the probability of event A and B is the number of outcomes in event A and B divided by the total number of outcomes.
P(A and B) = \frac{# of outcomes in A and B}{total # of outcomes}
 = \frac{3}{17}
The probability that a soup was ordered in a cup and was split pea is \frac{3}{17}.


Question: For a math assignment, students noted the number of times a wheel landed on the numbers 0 through 5. How many students spun 4?

Answer: 4

Solution:
Find the row for 4 and read the frequency. The frequency is 4.

4 students spun 4.


Question: Look at the following schedule. Betty got on the ferry at Windy Sands at 4.00 P.M. What time will she get to Foggy Port?

Choices:
- 5:00 P.M.
- 8:00 A.M.
- 5:15 P.M.
- 5:45 P.M.

Answer: 5:45 P.M.

Bay Harbor
Sandy Shores
Seagull Port
Cliff View
Green Harbor
Windy Sands
Foggy Port

Solution:
Find 4:00 P. M. in the row for Windy Sands. That column shows the schedule for the ferry that Betty is on.

Look down the column until you find the row for Foggy Port.

Betty will get to Foggy Port at 5:45 P. M.


Question: An archer recalled how many times he hit the bull's-eye in the past 7 days. What is the median of the numbers?

Answer: 6

Day | Number of bull's-eyes
Thursday | 8
Friday | 8
Saturday | 3
Sunday | 9
Monday | 6
Tuesday | 6
Wednesday | 4

Thursday Friday Saturday Sunday Monday Tuesday Wednesday

Solution:
Read the numbers from the table.

8, 8, 3, 9, 6, 6, 4

First, arrange the numbers from least to greatest:

3, 4, 6, 6, 8, 8, 9

Now find the number in the middle.

3, 4, 6, 6, 8, 8, 9

The number in the middle is 6.

The median is 6.


Question: Rita wants to buy 1 kilogram of Cavendish bananas, 3 kilograms of pink bananas, and 3 kilograms of red bananas. How much will she spend?

Answer: 6.20

Cavendish bananas | $0.98/kilogram
plantains | $0.98/kilogram
pink bananas | $1.09/kilogram
bananitos | $0.49/kilogram
red bananas | $0.65/kilogram

Cavendish bananas
plantains
pink bananas
bananitos
red bananas

Solution:
Find the cost of the Cavendish bananas. Multiply:

$0.98 × 1 = $0.98

Find the cost of the pink bananas. Multiply:

$1.09 × 3 = $3.27

Find the cost of the red bananas. Multiply:

$0.65 × 3 = $1.95

Now find the total cost by adding:

$0.98 + $3.27 + $1.95 = $6.20

She will spend $6.20.


Question: The table shows a function. Is the function linear or nonlinear?

Choices:
- linear
- nonlinear

Answer: nonlinear

Solution:
To determine whether the function is linear or nonlinear, see whether it has a constant rate of change.
Pick the points in any two rows of the table and calculate the rate of change between them. The first two rows are a good place to start.
Call the values in the first row x1 and y1. Call the values in the second row x2 and y2.
Rate of change = \frac{y2 - y1}{x2 - x1}
 = \frac{11 - 18}{17 - 16}
 = \frac{-7}{1}
 = -7
Now pick any other two rows and calculate the rate of change between them.
Call the values in the first row x1 and y1. Call the values in the third row x2 and y2.
Rate of change = \frac{y2 - y1}{x2 - x1}
 = \frac{8 - 18}{18 - 16}
 = \frac{-10}{2}
 = -5
The rate of change is not the same for each pair of points. So, the function does not have a constant rate of change.
The function is nonlinear.


Question: Ruben has $8.50. Does he have enough to buy a red pepper and a pumpkin?

Choices:
- yes
- no

Answer: no

cucumber | $1.30
pumpkin | $7.38
watermelon | $4.86
grapefruit | $1.20
red pepper | $1.25

cucumber
pumpkin
watermelon
grapefruit
red pepper

Solution:
Add the price of a red pepper and the price of a pumpkin:

$1.25 + $7.38 = $8.63

$8.63 is more than $8.50. Ruben does not have enough money.


Question: Look at the following schedule. At which stop does the train arrive at 12.30 P.M.?

Choices:
- shopping mall
- science museum
- art museum
- baseball stadium

Answer: baseball stadium

Location | Time
library | 10:30 A.M.
soccer field | 10:35 A.M.
town square | 10:55 A.M.
university | 11:20 A.M.
grocery store | 11:40 A.M.
swimming pool | 12:10 P.M.
baseball stadium | 12:30 P.M.
art museum | 12:35 P.M.
shopping mall | 12:55 P.M.
science museum | 1:10 P.M.

library
soccer field
town square
university
grocery store
swimming pool
baseball stadium
art museum
shopping mall
science museum

Solution: Find 12:30 P. M. on the schedule. The train arrives at the baseball stadium at 12:30 P. M.


Question: The Cedarburg Middle School fundraising committee found out how many sweatshirts students already had, in order to decide whether to sell sweatshirts for a fundraiser. How many students have at least 2 sweatshirts?

Answer: 30

Number of sweatshirts | Frequency
0 | 10
1 | 12
2 | 19
3 | 11

Solution:
Find the rows for 2 and 3 sweatshirts. Add the frequencies for these rows.

Add:

19 + 11 = 30

30 students have at least 2 sweatshirts.


Question: Look at the table. Then answer the question. At a price of $55, is there a shortage or a surplus?

Choices:
- shortage
- surplus

Answer: shortage

Solution: At the price of $55, the quantity demanded is greater than the quantity supplied. There is not enough of the good or service for sale at that price. So, there is a shortage.


Question: In considering whether to open a new branch, the city council examined the number of times some typical residents went to the library last month. How many people went to the library at least 2 times last month?

Answer: 16

Number of trips | Frequency
1 | 20
2 | 10
3 | 2
4 | 4

Solution:
Find the rows for 2, 3, and 4 times last month. Add the frequencies for these rows.

Add:

10 + 2 + 4 = 16

16 people went to the library at least 2 times last month.


Question: Look at this table. Is this relation a function?

Choices:
- yes
- no

Answer: yes

Solution:
Look at the x-values in the table.

Each of the x-values is paired with only one y-value, so the relation is a function.


Question: Each aquarium has 10 orange fish. How many orange fish are in 4 aquariums?

Answer: 40

Number of aquariums | Number of orange fish
1 | 10
2 | 20
3 | 30
4 | ?

Solution: Count by tens. Use the chart: there are 40 orange fish in 4 aquariums.


Question: Some friends played miniature golf and wrote down their scores. How many more strokes did Sandeep take than Erica?

Answer: 47

Name | Score
Marshall | 150
Barbara | 131
Darius | 114
Erica | 128
Sandeep | 175

Solution:
Find the numbers in the table.

Sandeep: 175
Erica: 128

Now subtract: 175 - 128 = 47.

Sandeep took 47 more strokes.


Question: The table shows a function. Is the function linear or nonlinear?

Choices:
- linear
- nonlinear

Answer: nonlinear

Solution:
To determine whether the function is linear or nonlinear, see whether it has a constant rate of change.
Pick the points in any two rows of the table and calculate the rate of change between them. The first two rows are a good place to start.
Call the values in the first row x1 and y1. Call the values in the second row x2 and y2.
Rate of change = \frac{y2 - y1}{x2 - x1}
 = \frac{13 - 14}{15 - 14}
 = \frac{-1}{1}
 = -1
Now pick any other two rows and calculate the rate of change between them.
Call the values in the second row x1 and y1. Call the values in the third row x2 and y2.
Rate of change = \frac{y2 - y1}{x2 - x1}
 = \frac{7 - 13}{16 - 15}
 = \frac{-6}{1}
 = -6
The rate of change is not the same for each pair of points. So, the function does not have a constant rate of change.
The function is nonlinear.


Question: A reporter looked through her notebook to remember how many people she had interviewed in the past 7 days. What is the mean of the numbers?

Answer: 13

Day | Number of people
Sunday | 19
Monday | 12
Tuesday | 12
Wednesday | 21
Thursday | 8
Friday | 7
Saturday | 12

Sunday Monday Tuesday Wednesday Thursday Friday Saturday

Solution:
Read the numbers from the table.

19, 12, 12, 21, 8, 7, 12

First, count how many numbers are in the group.

There are 7 numbers.

Now add all the numbers together:

19 + 12 + 12 + 21 + 8 + 7 + 12 = 91

Now divide the sum by the number of numbers:

91 ÷ 7 = 13

The mean is 13.


Question: Mona spent a week at the beach and recorded the number of shells she found each day. According to the table, what was the rate of change between Tuesday and Wednesday?

Answer: -2

Day | Number of shells
Tuesday | 2
Wednesday | 0
Thursday | 3
Friday | 6
Saturday | 1

Tuesday Wednesday Thursday Friday Saturday

Solution:
Plug the numbers into the formula for rate of change and simplify.
Rate of change
 = \frac{change in value}{change in time}
 = \frac{0 shells - 2 shells}{1 day}
 = \frac{-2 shells}{1 day}
 = -2 shells per day
The rate of change between Tuesday and Wednesday was - 2 shells per day.


Question: What is the total cost for 3/10 of a pound of crab meat?

Answer: 1.80

shrimp | $8 per pound
crab meat | $6 per pound
oysters | $10 per pound
scallops | $5 per pound
lobster meat | $6 per pound
mussels | $3 per pound

shrimp
crab meat
oysters
scallops
lobster meat
mussels

$8 per pound
$6 per pound
$10 per pound
$5 per pound
$6 per pound
$3 per pound

Solution:
Find the cost of the crab meat. Multiply the price per pound by the number of pounds.
$6 × \frac{3}{10} = $6 × 0.3 = $1.80
The total cost is $1.80.


Question: A researcher recorded the number of cows on each farm in the county. How many farms have exactly 25 cows?

Answer: 2

Solution:
For the number 25, the stem is 2, and the leaf is 5. Find the row where the stem is 2. In that row, count all the leaves equal to 5.

You counted 2 leaves, which are blue in the stem-and-leaf plot above. 2 farms have exactly25 cows.


Question: Look at the following schedule. When does the men's vault event end?

Choices:
- 2:45 P.M.
- 1:40 P.M.
- 2:30 P.M.
- 1:45 P.M.

Answer: 2:30 P.M.

Event | Begin | End
men's parallel bars | 11:30 A.M. | 12:05 P.M.
women's balance beam | 12:20 P.M. | 12:55 P.M.
men's floor exercise | 12:50 P.M. | 1:40 P.M.
men's vault | 1:45 P.M. | 2:30 P.M.
men's rings | 2:30 P.M. | 2:50 P.M.
men's pommel horse | 2:35 P.M. | 3:00 P.M.
men's high bar | 2:45 P.M. | 3:45 P.M.

men's parallel bars
women's balance beam
men's floor exercise
men's vault
men's rings
men's pommel horse
men's high bar

Solution:
Find the men's vault event on the schedule. Find the end time for the men's vault event.

men's vault: 2:30 P. M.


Question: Bryant has $1,544.00. Does he have enough to buy an African safari vacation package and a Jamaican vacation package?

Choices:
- yes
- no

Answer: no

European vacation package | $643.00
Caribbean vacation package | $839.00
African safari vacation package | $962.00
Jamaican vacation package | $608.00

European vacation package
Caribbean vacation package
African safari vacation package
Jamaican vacation package

Solution:
Add the price of an African safari vacation package and the price of a Jamaican vacation package:

$962.00 + $608.00 = $1,570.00

$1,570.00 is more than $1,544.00. Bryant does not have enough money.


Question: For a fundraiser, the children in the art club made greeting cards and kept track of how many they produced. How many children made more than 1 greeting card?

Answer: 36

Greeting cards made | Frequency
0 | 14
1 | 12
2 | 17
3 | 4
4 | 15

Solution:
Find the rows for 2, 3, and 4 greeting cards. Add the frequencies for these rows.

Add:

17 + 4 + 15 = 36

36 children made more than 1 greeting card.


Question: Mr. Middleton, a track coach, recorded the sizes of all the nearby track teams. How many teams have at least 27 members?

Answer: 16

Solution:
Find the row with stem 2. Count all the leaves greater than or equal to 7.

Count all the leaves in the rows with stems 3, 4, 5, 6, 7, and 8.

You counted 16 leaves, which are blue in the stem-and-leaf plots above. 16 teams have at least 27 members.


Question: Some friends played a trivia game and recorded their scores. What is the mode of the numbers?

Answer: 55

Name | Score
Vijay | 46
Scott | 55
Bob | 55
Jason | 46
Heather | 48
Charlie | 55
Aiden | 48

Vijay Scott Bob Jason Heather Charlie Aiden

Solution:
Read the numbers from the table.

46, 55, 55, 46, 48, 55, 48

First, arrange the numbers from least to greatest:

46, 46, 48, 48, 55, 55, 55

Now count how many times each number appears.

46 appears 2 times.
48 appears 2 times.
55 appears 3 times.

The number that appears most often is 55.

The mode is 55.


Question: Ariel is looking at the price of new cell phones online. Her favorite company, OrangeTech, has a special this weekend. Ariel can add an upgrade to a phone for an additional cost, or she can buy a used phone to get a discount. The change in price for each option is shown in the table. Which option results in a greater change in price?

Choices:
- adding an upgrade
- buying a used phone

Answer: buying a used phone

Option | Change in phone price
Add an upgrade | $60
Buy a used phone | -$75

Solution:
To find the option that results in a greater change in price, use absolute value. Absolute value tells you how much the price changes.
Add an upgrade: |$60| = $60
Buy a used phone: |-$75| = $75
Buying a used phone results in a greater change in price. It reduces the price by $75.


Question: Look at the table. Then answer the question. At a price of $180, is there a shortage or a surplus?

Choices:
- shortage
- surplus

Answer: surplus

Solution: At the price of $180, the quantity demanded is less than the quantity supplied. There is too much of the good or service for sale at that price. So, there is a surplus.


Question: Each branch has 5 caterpillars. How many caterpillars are on 5 branches?

Answer: 25

Number of branches | Number of caterpillars
1 | 5
2 | 10
3 | 15
4 | 20
5 | ?

Solution: Count by fives. Use the chart: there are 25 caterpillars on 5 branches.


Question: Lena joined a book club to spend more quality time with her cousin. At the first meeting, club members recorded how many hours a week they typically read and whether they preferred e-readers or paperback books. What is the probability that a randomly selected club member reads about 3 hours per week and prefers e-readers? Simplify any fractions.

Answer: 1/3

 | E-readers | Paperback books
About 1 hour per week | 3 | 6
About 3 hours per week | 6 | 3

About 1 hour per week
About 3 hours per week

Solution:
Let A be the event "the club member reads about 3 hours per week" and B be the event "the club member prefers e-readers".
To find the probability that a club member reads about 3 hours per week and prefers e-readers, first identify the sample space and the event.
The outcomes in the sample space are the different club members. Each club member is equally likely to be selected, so this is a uniform probability model.
The event is A and B, "the club member reads about 3 hours per week and prefers e-readers".
Since this is a uniform probability model, count the number of outcomes in the event A and B and count the total number of outcomes. Then, divide them to compute the probability.

Find the number of outcomes in the event A and B.
A and B is the event "the club member reads about 3 hours per week and prefers e-readers", so look at the table to see how many club members read about 3 hours per week and prefer e-readers.
The number of club members who read about 3 hours per week and prefer e-readers is 6.

Find the total number of outcomes.
Add all the numbers in the table to find the total number of club members.
3 + 6 + 6 + 3 = 18

Find P(A and B).
Since all outcomes are equally likely, the probability of event A and B is the number of outcomes in event A and B divided by the total number of outcomes.
P(A and B) = \frac{# of outcomes in A and B}{total # of outcomes}
 = \frac{6}{18}
 = \frac{1}{3}
The probability that a club member reads about 3 hours per week and prefers e-readers is \frac{1}{3}.


Question: How much money does Laura need to buy 8 designer watches and 8 designer ball gowns?

Answer: 56,672

designer coat | $6,487.00
designer watch | $5,254.00
designer ball gown | $1,830.00
designer handbag | $2,288.00
pair of designer boots | $1,906.00
pair of designer shoes | $8,293.00

designer coat
designer watch
designer ball gown
designer handbag
pair of designer boots
pair of designer shoes

Solution:
Find the cost of 8 designer watches.

$5,254.00 × 8 = $42,032.00

Find the cost of 8 designer ball gowns.

$1,830.00 × 8 = $14,640.00

Now find the total cost.

$42,032.00 + $14,640.00 = $56,672.00

Laura needs $56,672.00.


Question: Savannah works at a coffee shop on weekends. Every now and then, a customer will order a hot tea and ask Savannah to surprise them with the flavor. The teas are categorized by flavor and caffeine level. What is the probability that a randomly selected tea is caffeine-free and mint? Simplify any fractions.

Answer: 1/5

 | Mint | Fruity
Caffeine-free | 3 | 5
Caffeinated | 2 | 5

Solution:
Let A be the event "the tea is caffeine-free" and B be the event "the tea is mint".
To find the probability that a tea is caffeine-free and mint, first identify the sample space and the event.
The outcomes in the sample space are the different teas. Each tea is equally likely to be selected, so this is a uniform probability model.
The event is A and B, "the tea is caffeine-free and mint".
Since this is a uniform probability model, count the number of outcomes in the event A and B and count the total number of outcomes. Then, divide them to compute the probability.

Find the number of outcomes in the event A and B.
A and B is the event "the tea is caffeine-free and mint", so look at the table to see how many teas are caffeine-free and mint.
The number of teas that are caffeine-free and mint is 3.

Find the total number of outcomes.
Add all the numbers in the table to find the total number of teas.
3 + 2 + 5 + 5 = 15

Find P(A and B).
Since all outcomes are equally likely, the probability of event A and B is the number of outcomes in event A and B divided by the total number of outcomes.
P(A and B) = \frac{# of outcomes in A and B}{total # of outcomes}
 = \frac{3}{15}
 = \frac{1}{5}
The probability that a tea is caffeine-free and mint is \frac{1}{5}.


Question: Wildgrove Flooring tracked the number of broken tiles in each shipment it received last year. What is the smallest number of broken tiles?

Answer: 22

Solution:
Look at the first row of the stem-and-leaf plot. The first row has the lowest stem. The stem for the first row is 2.

Now find the lowest leaf in the first row. The lowest leaf is 2.

The smallest number of broken tiles has a stem of 2 and a leaf of 2. Write the stem first, then the leaf: 22.

The smallest number of broken tiles is 22 broken tiles.


Question: To get credit for meeting her school's community service requirement, Lola kept a volunteering log. What is the median of the numbers?

Answer: 6

Day | Hours
Thursday | 4
Friday | 8
Saturday | 6
Sunday | 2
Monday | 10

Solution:
Read the numbers from the table.

4, 8, 6, 2, 10

First, arrange the numbers from least to greatest:

2, 4, 6, 8, 10

Now find the number in the middle.

2, 4, 6, 8, 10

The number in the middle is 6.

The median is 6.


Question: Irma's classmates revealed how many science articles they read. Who read the fewest science articles?

Choices:
- Irma
- Rose
- Carmen
- Hugo

Answer: Rose

Name | Number of science articles
Irma | 659
Rose | 635
Carmen | 638
Hugo | 665

Solution:
Find the least number in the table. Remember to compare the numbers starting with the highest place value. The least number is 635.

Now find the corresponding name. Rose corresponds to 635.


Question: As part of a math lab, Rosanne tracked the number of times her classmates drew a number between 2 and 8. Which number was drawn the fewest times?

Answer: 7

Solution: Look at the frequency column. Find the least frequency. The least frequency is 0, which is in the row for 7. 7 was drawn the fewest times.


Question: Sparrowtown High School's student council recruited teachers and students to serve on each of its committees. Are there fewer people on the party committee or the cafeteria committee?

Choices:
- cafeteria
- party

Answer: cafeteria

Committee | Students | Teachers
Cafeteria | 13 | 7
Party | 18 | 16
Sports | 13 | 8
Graduation | 9 | 15

Solution:
Add the numbers in the Party row. Then, add the numbers in the Cafeteria row.

party: 18 + 16 = 34
cafeteria: 13 + 7 = 20

20 is less than 34. Fewer people are on the cafeteria committee.


Question: The advertising agency counted the number of billboards in each city in the state. What is the largest number of billboards?

Answer: 56

Solution:
Look at the last row of the stem-and-leaf plot. The last row has the highest stem. The stem for the last row is 5.

Now find the highest leaf in the last row. The highest leaf is 6.

The largest number of billboards has a stem of 5 and a leaf of 6. Write the stem first, then the leaf: 56.

The largest number of billboards is 56 billboards.


Question: Derek bought 1.3 pounds of pepper. How much did he spend?

Answer: 10.40

pepper | $8 per lb
cinnamon | $7 per lb
turmeric | $6 per lb
cumin | $8 per lb
paprika | $4 per lb

$8 per lb
$7 per lb
$6 per lb
$8 per lb
$4 per lb

Solution:
Find the cost of the pepper. Multiply the price per pound by the number of pounds.
$8 × 1.3 = $10.40
He spent $10.40.


Question: Compare pattern A to pattern B. Which statement is true?

Choices:
- Each term in pattern B can be found by subtracting the corresponding term in pattern A from 28.
- Each term in pattern B can be found by multiplying the corresponding term in pattern A by 4 and then subtracting 2.

Answer: Each term in pattern B can be found by multiplying the corresponding term in pattern A by 4 and then subtracting 2.

Solution:
Look at the corresponding terms in the table. For example, the first pair of corresponding terms is 6 and 22.
Read the first statement.
Each term in pattern B can be found by subtracting the corresponding term in pattern A from 28.
This statement is not true for all of the corresponding terms. For example, 30 is not equal to 8 subtracted from 28.
Read the second statement.
Each term in pattern B can be found by multiplying the corresponding term in pattern A by 4 and then subtracting 2.
This statement is true for all of the corresponding terms.
6 × 4 = 24, and then 24 - 2 = 22
8 × 4 = 32, and then 32 - 2 = 30
10 × 4 = 40, and then 40 - 2 = 38
12 × 4 = 48, and then 48 - 2 = 46


Question: A law firm in Kensington kept track of how many hours were billed by each partner last year. What fraction of the hours were billed by Bob? Simplify your answer.

Answer: 93/517

Partner | Hours billed
Kendall | 760
Melissa | 910
Allie | 1,000
Bob | 930
Gordon | 820
Gina | 750

Solution:
Find how many hours were billed by Bob.

930

Find how many hours were billed in total.

760 + 910 + 1,000 + 930 + 820 + 750 = 5,170

Divide 930 by 5,170.

\frac{930}{5,170}

Reduce the fraction.

\frac{930}{5,170} → \frac{93}{517}

\frac{93}{517} of hours were billed by Bob.


Question: The members of the science club shared how many times they had been to the zoo last year. How many members went to the zoo more than 3 times?

Answer: 8

Number of trips | Frequency
0 | 13
1 | 4
2 | 16
3 | 0
4 | 3
5 | 5

Solution:
Find the rows for 4 and 5 times. Add the frequencies for these rows.

Add:

3 + 5 = 8

8 members went to the zoo more than 3 times.


Question: How much money does Cody need to buy 5 jars of olives?

Answer: 2.10

jar of pickles | $0.87
jar of olives | $0.42
can of mushrooms | $0.95
jar of applesauce | $0.88

jar of pickles
jar of olives
can of mushrooms
jar of applesauce

Solution:
Find the total cost of 5 jars of olives by multiplying 5 times the price of a jar of olives.

$0.42 × 5 = $2.10

Cody needs $2.10.


Question: A stock broker followed the stock prices of a certain set of companies. On Wednesday, how much more did Thompson Corporation's stock cost than Houston Sporting Goods's stock?

Answer: 5

Company | Wednesday | Thursday
Thompson Corporation | $19 | $18
Watson and Partners | $20 | $6
Computer Data Company | $4 | $18
White and Company | $14 | $12
Houston Sporting Goods | $14 | $13

Thompson Corporation
Watson and Partners
Computer Data Company
White and Company
Houston Sporting Goods

Solution:
Find the Wednesday column. Find the numbers in this column for Thompson Corporation and Houston Sporting Goods.

Thompson Corporation: $19.00
Houston Sporting Goods: $14.00

Now subtract:

$19.00 − $14.00 = $5.00

On Wednesday Thompson Corporation's stock cost $5 more than Houston Sporting Goods's stock.


Question: A researcher asked people how many letters they had written in the past year and recorded the results. How many people did not write letters?

Answer: 3

Letters written | Frequency
0 | 3
1 | 16
2 | 9
3 | 6

Solution:
Find the row for 0 letters and read the frequency. The frequency is 3.

3 people did not write letters.


Question: Miguel has $6.00. Does he have enough to buy a book about dinosaurs and a book about helicopters?

Choices:
- yes
- no

Answer: yes

book about helicopters | $2.00
book about reptiles | $6.00
book about dinosaurs | $3.00
book about outer space | $1.00

book about helicopters
book about reptiles
book about dinosaurs
book about outer space

Solution:
Add the price of a book about dinosaurs and the price of a book about helicopters:

$3.00 + $2.00 = $5.00

$5.00 is less than $6.00. Miguel does have enough money.


Question: A survey was conducted to learn people's chocolate preferences. What fraction of the respondents preferred milk chocolate? Simplify your answer.

Answer: 53/201

Type | Number of respondents
Dark chocolate | 480
Milk chocolate | 530
White chocolate | 1,000

Dark chocolate
Milk chocolate
White chocolate

Solution:
Find how many respondents preferred milk chocolate.

530

Find how many people responded in total.

480 + 530 + 1,000 = 2,010

Divide 530 by2,010.

\frac{530}{2,010}

Reduce the fraction.

\frac{530}{2,010} → \frac{53}{201}

\frac{53}{201} of respondents preferred milk chocolate.


Question: Brett, who has five different fruit trees growing in his yard, kept track of how many pieces of fruit he picked this year. What fraction of the pieces of fruit picked were pears? Simplify your answer.

Answer: 11/56

Fruits | Pieces of fruit
Lemons | 41
Nectarines | 100
Apples | 71
Plums | 13
Pears | 55

Solution:
Find how many pears were picked.

55

Find how many pieces of fruit were picked in total.

41 + 100 + 71 + 13 + 55 = 280

Divide 55 by280.

\frac{55}{280}

Reduce the fraction.

\frac{55}{280} → \frac{11}{56}

\frac{11}{56} of pears were picked.


Question: A researcher recorded the number of cows on each farm in the county. How many farms have at least 70 cows but fewer than 100 cows?

Answer: 3

Solution:
Count all the leaves in the rows with stems 7, 8, and 9.

You counted 3 leaves, which are blue in the stem-and-leaf plot above. 3 farms have at least 70 cows but fewer than 100 cows.


Question: To figure out how many vacation days she had left to use, Abby looked over her old calendars to figure out how many days of vacation she had taken each year. According to the table, what was the rate of change between 2014 and 2015?

Answer: -5

Solution:
Plug the numbers into the formula for rate of change and simplify.
Rate of change
 = \frac{change in value}{change in time}
 = \frac{34 vacation days - 39 vacation days}{2015 - 2014}
 = \frac{34 vacation days - 39 vacation days}{1 year}
 = \frac{-5 vacation days}{1 year}
 = -5 vacation days per year
The rate of change between 2014 and 2015 was - 5 vacation days per year.


Question: Look at the table. Then answer the question. At a price of $180, is there a shortage or a surplus?

Choices:
- shortage
- surplus

Answer: shortage

Solution: At the price of $180, the quantity demanded is greater than the quantity supplied. There is not enough of the good or service for sale at that price. So, there is a shortage.


Question: Derek has $0.13. Does he have enough to buy a spiral snail shell and a pink and white striped shell?

Choices:
- yes
- no

Answer: yes

purple clam shell | $0.07
white spindle shell | $0.07
spiral snail shell | $0.05
scallop shell | $0.01
pink and white striped shell | $0.07

purple clam shell
white spindle shell
spiral snail shell
scallop shell
pink and white striped shell

Solution:
Add the price of a spiral snail shell and the price of a pink and white striped shell:

$0.05 + $0.07 = $0.12

$0.12 is less than $0.13. Derek does have enough money.


Question: Chad looked at the dates of the digital photos on his computer to find out how many he had taken in the past 5 days. What is the mean of the numbers?

Answer: 5

Day | Number of photographs
Saturday | 6
Sunday | 0
Monday | 8
Tuesday | 3
Wednesday | 8

Saturday Sunday Monday Tuesday Wednesday

Solution:
Read the numbers from the table.

6, 0, 8, 3, 8

First, count how many numbers are in the group.

There are 5 numbers.

Now add all the numbers together:

6 + 0 + 8 + 3 + 8 = 25

Now divide the sum by the number of numbers:

25 ÷ 5 = 5

The mean is 5.


Question: Natalie just returned from a spring break volunteer trip. She is shopping for a photo album that will showcase her photos from the trip. The albums range in photo capacity and orientation. What is the probability that a randomly selected photo album holds exactly 100 photos and is oriented horizontally? Simplify any fractions.

Answer: 1/9

 | Horizontally | Vertically
50 photos | 8 | 5
100 photos | 2 | 3

Solution:
Let A be the event "the photo album holds exactly100 photos" and B be the event "the photo album is oriented horizontally".
To find the probability that a photo album holds exactly100 photos and is oriented horizontally, first identify the sample space and the event.
The outcomes in the sample space are the different photo albums. Each photo album is equally likely to be selected, so this is a uniform probability model.
The event is A and B, "the photo album holds exactly100 photos and is oriented horizontally".
Since this is a uniform probability model, count the number of outcomes in the event A and B and count the total number of outcomes. Then, divide them to compute the probability.

Find the number of outcomes in the event A and B.
A and B is the event "the photo album holds exactly100 photos and is oriented horizontally", so look at the table to see how many photo albums hold exactly100 photos and are oriented horizontally.
The number of photo albums that hold exactly100 photos and are oriented horizontally is 2.

Find the total number of outcomes.
Add all the numbers in the table to find the total number of photo albums.
8 + 2 + 5 + 3 = 18

Find P(A and B).
Since all outcomes are equally likely, the probability of event A and B is the number of outcomes in event A and B divided by the total number of outcomes.
P(A and B) = \frac{# of outcomes in A and B}{total # of outcomes}
 = \frac{2}{18}
 = \frac{1}{9}
The probability that a photo album holds exactly100 photos and is oriented horizontally is \frac{1}{9}.


Question: Rosa, a journalism student, counted the number of pages in several major magazines. How many magazines had exactly 26 pages?

Answer: 3

Solution:
For the number 26, the stem is 2, and the leaf is 6. Find the row where the stem is 2. In that row, count all the leaves equal to 6.

You counted 3 leaves, which are blue in the stem-and-leaf plot above. 3 magazines had exactly26 pages.


Question: Look at the following schedule. When does the discus throw end?

Choices:
- 11:45 A.M.
- 2:25 P.M.
- 1:45 P.M.
- 12:40 P.M.

Answer: 1:45 P.M.

Event | Begin | End
javelin throw | 11:00 A.M. | 11:15 A.M.
steeplechase | 11:30 A.M. | 11:45 A.M.
men's relay | 11:50 A.M. | 12:40 P.M.
discus throw | 12:45 P.M. | 1:45 P.M.
pole vault | 1:55 P.M. | 2:25 P.M.
long jump | 2:40 P.M. | 3:15 P.M.

javelin throw
steeplechase
men's relay
discus throw
pole vault
long jump

Solution:
Find the discus throw on the schedule. Find the end time for the discus throw.

discus throw: 1:45 P. M.


Question: How much money does Darnel need to buy a black motorcycle, a red two-door coupe, and a black convertible?

Answer: 23,520

red sports car | $8,473.00
black motorcycle | $9,734.00
red two-door coupe | $7,702.00
black convertible | $6,084.00
old white van | $8,178.00
dark blue hatchback | $5,038.00

red sports car
black motorcycle
red two-door coupe
black convertible
old white van
dark blue hatchback

Solution:
Find the total cost of a black motorcycle, a red two-door coupe, and a black convertible.

$9,734.00 + $7,702.00 + $6,084.00 = $23,520.00

Darnel needs $23,520.00.


Question: The art club examined how many cookies each student baked for the bake sale. Who baked the most cookies?

Choices:
- Riley
- Hannah
- Layla
- Madelyn

Answer: Madelyn

Name | Number of cookies
Riley | 71
Hannah | 75
Layla | 78
Madelyn | 79

Solution:
Find the greatest number in the table. Remember to compare the numbers starting with the highest place value. The greatest number is 79.

Now find the corresponding name. Madelyn corresponds to 79.


Question: Terrell has $14.49. How much money will Terrell have left if he buys a can of coffee beans and a block of cheddar cheese?

Answer: 5.86

bag of marshmallows | $2.97
bag of chocolate chips | $2.61
block of cheddar cheese | $3.47
can of coffee beans | $5.16
bag of almonds | $4.05

bag of marshmallows
bag of chocolate chips
block of cheddar cheese
can of coffee beans
bag of almonds

Solution:
Find the total cost of a can of coffee beans and a block of cheddar cheese.

$5.16 + $3.47 = $8.63

Now subtract the total cost from the starting amount.

$14.49 - $8.63 = $5.86

Terrell will have $5.86 left.


Question: A skating rink attendant monitored the number of injuries at the rink over the past year. He tracked the ages of those injured and the kinds of skates worn during injury. What is the probability that a randomly selected injured skater was wearing in-line skates and was age 8? Simplify any fractions.

Answer: 1/5

 | Age 8 | Age 10
In-line skates | 2 | 3
Roller skates | 2 | 3

Solution:
Let A be the event "the injured skater was wearing in-line skates" and B be the event "the injured skater was age 8".
To find the probability that a injured skater was wearing in-line skates and was age 8, first identify the sample space and the event.
The outcomes in the sample space are the different injured skaters. Each injured skater is equally likely to be selected, so this is a uniform probability model.
The event is A and B, "the injured skater was wearing in-line skates and was age 8".
Since this is a uniform probability model, count the number of outcomes in the event A and B and count the total number of outcomes. Then, divide them to compute the probability.

Find the number of outcomes in the event A and B.
A and B is the event "the injured skater was wearing in-line skates and was age 8", so look at the table to see how many injured skaters were wearing in-line skates and were age 8.
The number of injured skaters who were wearing in-line skates and were age 8 is 2.

Find the total number of outcomes.
Add all the numbers in the table to find the total number of injured skaters.
2 + 2 + 3 + 3 = 10

Find P(A and B).
Since all outcomes are equally likely, the probability of event A and B is the number of outcomes in event A and B divided by the total number of outcomes.
P(A and B) = \frac{# of outcomes in A and B}{total # of outcomes}
 = \frac{2}{10}
 = \frac{1}{5}
The probability that a injured skater was wearing in-line skates and was age 8 is \frac{1}{5}.


Question: Nolan has $1,425.00. Does he have enough to buy a wetsuit and a mountain bike?

Choices:
- yes
- no

Answer: yes

set of golf clubs | $390.00
snowboard | $910.00
mountain bike | $763.00
wetsuit | $660.00

set of golf clubs
snowboard
mountain bike
wetsuit

Solution:
Add the price of a wetsuit and the price of a mountain bike:

$660.00 + $763.00 = $1,423.00

$1,423.00 is less than $1,425.00. Nolan does have enough money.


Question: Reba buys 2.6 pounds of liverwurst. How much does she spend?

Answer: 10.40

salami | $2 per pound
liverwurst | $4 per pound
linguica | $4 per pound
pepperoni | $5 per pound
chorizo | $2 per pound
Italian sausage | $6 per pound
bratwurst | $6 per pound

salami
liverwurst
linguica
pepperoni
chorizo
Italian sausage
bratwurst

$2 per pound
$4 per pound
$4 per pound
$5 per pound
$2 per pound
$6 per pound
$6 per pound

Solution:
Find the cost of the liverwurst. Multiply the price per pound by the number of pounds.
$4 × 2.6 = $10.40
She spends $10.40.


Question: The teachers at a middle school counted how many computers they had in their classrooms. What is the mode of the numbers?

Answer: 6

Teacher | Number of computers
Ms. Rojas | 6
Ms. Cohen | 4
Mr. Lim | 5
Mrs. Rossi | 6
Mr. Morales | 9
Mr. Schmidt | 4
Miss Murphy | 6
Mrs. Tan | 5

Ms. Rojas
Ms. Cohen
Mr. Lim
Mrs. Rossi
Mr. Morales
Mr. Schmidt
Miss Murphy
Mrs. Tan

Solution:
Read the numbers from the table.

6, 4, 5, 6, 9, 4, 6, 5

First, arrange the numbers from least to greatest:

4, 4, 5, 5, 6, 6, 6, 9

Now count how many times each number appears.

4 appears 2 times.
5 appears 2 times.
6 appears 3 times.
9 appears 1 time.

The number that appears most often is 6.

The mode is 6.


Question: Sally looked at the dates of the digital photos on her computer to find out how many she had taken in the past 7 days. What is the mean of the numbers?

Answer: 6

Day | Number of photographs
Sunday | 0
Monday | 7
Tuesday | 4
Wednesday | 8
Thursday | 5
Friday | 12
Saturday | 6

Solution:
Read the numbers from the table.

0, 7, 4, 8, 5, 12, 6

First, count how many numbers are in the group.

There are 7 numbers.

Now add all the numbers together:

0 + 7 + 4 + 8 + 5 + 12 + 6 = 42

Now divide the sum by the number of numbers:

42 ÷ 7 = 6

The mean is 6.


Question: A concession stand worker at the movie theater looked up how many bags of popcorn were sold in the past 7 days. What is the range of the numbers?

Answer: 7

Day | Number of bags of popcorn
Friday | 1
Saturday | 6
Sunday | 3
Monday | 2
Tuesday | 3
Wednesday | 3
Thursday | 8

Friday Saturday Sunday Monday Tuesday Wednesday Thursday

Solution:
Read the numbers from the table.

1, 6, 3, 2, 3, 3, 8

First, find the greatest number. The greatest number is 8.

Next, find the least number. The least number is 1.

Subtract the least number from the greatest number:

8 − 1 = 7

The range is 7.


Question: A stock broker followed the stock prices of a certain set of companies. Which company's stock cost more on Wednesday, Watson and Partners or White and Company?

Choices:
- White and Company
- Watson and Partners

Answer: White and Company

Company | Wednesday | Thursday
Watson and Partners | $17 | $18
White and Company | $19 | $16
Jonas Incorporated | $20 | $18

Watson and Partners
White and Company
Jonas Incorporated

Solution:
Find the Wednesday column. Compare the numbers in this column for Watson and Partners and White and Company.

$19.00 is more than $17.00. On Wednesday, White and Company's stock cost more.


Question: Look at the following schedule. Linda got on the boat at Fisherman's Cove at 9.45 A.M. What time will she get to Palm Tree Island?

Choices:
- 1:45 P.M.
- 9:45 A.M.
- 10:45 A.M.
- 1:15 P.M.

Answer: 1:15 P.M.

Sea Town
Fisherman's Cove
Starfish Point
Rocky Cliffs
Palm Tree Island

Solution:
Find 9:45 A. M. in the row for Fisherman's Cove. That column shows the schedule for the boat that Linda is on.

Look down the column until you find the row for Palm Tree Island.

Linda will get to Palm Tree Island at 1:15 P. M.


Question: Joseph, an employee at Morrison's Convenience Store, looked at the sales of each of its soda products. How much more did the convenience store make from Nature's Nectar sales on Friday than on Thursday?

Answer: 2

Beverage | Thursday | Friday
Natural Goodness Juice | $18 | $10
Pearl's Soda | $7 | $4
Nature's Nectar | $2 | $4
Brenner's Juices | $5 | $13

Natural Goodness Juice
Pearl's Soda
Nature's Nectar
Brenner's Juices

Solution:
Find the Nature's Nectar row. Find the numbers in this row for Friday and Thursday.

Friday: $4.00
Thursday: $2.00

Now subtract:

$4.00 − $2.00 = $2.00

The convenience store made $2 more from Nature's Nectar sales on Friday than on Thursday.