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Math Problems
Algebra 2
Counting principle
Tommy and his mom are planting vegetables in their garden. Tommy has finished planting
5
5
5
rows of carrots so far and is planting new rows at a rate of
1
1
1
row per hour. His mom has finished
2
2
2
rows of tomatoes and will continue planting at
2
2
2
rows per hour. Once the pair get to the point where they have finished the same number of rows, they will take a break and decide what to plant next. How many rows will they each have completed?
\newline
Write a system of equations, graph them, and type the solution.
\newline
____ rows
\newline
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Max is going to order a breakfast platter at The Breakfast Club. He can choose one style of eggs, one type of meat, and one kind of toast. The following table shows the options available to him.
\newline
Breakfast platter Egg options: Fried, Scrambled, Poached
\newline
Hard boiled Meat options: Bacon, Sausage, Ham
\newline
Steak Toast options: White, Wheat, Rye
\newline
How many different breakfast platters could Max create?
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Luis is packing a bag for vacation. He has
9
9
9
unique shirts, but he can only fit
5
5
5
in his bag.
\newline
How many different groups of
5
5
5
shirts can he take?
\newline
◻
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Shurley bought a new bed and now needs to find pillows, sheets, and a comforter for it. She wants to have black or white pillows; striped or plaid sheets; and a solid, polka-dot, or zebra-print comforter.
\newline
How many unique bedding combinations can Shurley make?
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Edwin needs to buy a car, a truck, and a motorcycle for his shipping business. He wants the car to be red or yellow; the truck to be black, white, or silver; and the motorcycle to be green, blue, or orange.
\newline
How many different combinations of vehicles does Edwin have to choose from?
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Bruce and Krista are going to buy a new furniture set for their living room. They want to buy a couch, a coffee table, and a recliner. They have narrowed it down so that they are choosing between
4
4
4
couches,
5
5
5
coffee tables, and
9
9
9
recliners.
\newline
How many different furniture combinations are possible?
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Brunette College offers
4
4
4
math classes,
2
2
2
science classes,
3
3
3
language classes, and
5
5
5
art classes. Sylvia needs to sign up for exactly one class in each subject.
\newline
How many different combinations of classes does Sylvia have to choose from?
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Oula is going on an outdoor expedition with his family. The expedition will include a hunting event, a fishing event, a hiking event, and a camping event. There are
4
4
4
hunting,
7
7
7
fishing,
6
6
6
hiking, and
3
3
3
camping events for Oula's family to choose from.
\newline
How many different outdoor expeditions are possible?
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Paula is going to choose the size, color, phrase, and picture for a birthday card for her friend. There are
2
2
2
sizes,
4
4
4
colors,
7
7
7
phrases, and
4
4
4
pictures for her to choose from. (The printing company charges a fee to add extra design elements, so she will choose only one of each.)
\newline
How many different card designs are possible?
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Billy is picking a sandwich, a snack, a dessert, and a drink for his lunch. He can have a ham, turkey, or salami sandwich; an apple, banana, or carrots for his snack; a cookie or brownie for his dessert; and apple or orange juice for his drink.
\newline
How many different lunch combinations does Billy have to choose from?
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Bruno is designing his next skateboard. The skateboard store has
3
3
3
types of grip tape,
13
13
13
types of decks,
7
7
7
types of trucks,
4
4
4
types of bearings, and
2
2
2
types of wheels.
\newline
How many different skateboards can Bruno create? Assume each skateboard will contain only one type of each component.
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Sebastian is going to choose the color, pattern, font, and image for the design of a sweatshirt for his dance team. There are
10
10
10
colors,
4
4
4
patterns,
12
12
12
fonts, and
9
9
9
images for him to choose from. (The printing company charges a fee to add extra design elements, so he will choose only one of each.)
\newline
How many different sweatshirt designs are possible?
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Rossi is planning a date with his girlfriend. He plans for them to watch a movie, go out to dinner, and then attend a sporting event. He is deciding between
5
5
5
movies,
8
8
8
restaurants, and
2
2
2
sporting events.
\newline
How many different dates can Rossi plan?
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John always wears a shirt, pants, socks, and shoes. He owns
12
12
12
pairs of socks,
3
3
3
pairs of shoes,
5
5
5
pairs of pants, and
5
5
5
shirts.
\newline
How many different outfits can John make?
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Carlos is almost old enough to go to school! Based on where he lives, there are
6
6
6
elementary schools,
3
3
3
middle schools, and
2
2
2
high schools that he has the option of attending.
\newline
How many different education paths are available to Carlos? Assume he will attend only one of each type of school.
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A committee must be formed with
2
2
2
teachers and
3
3
3
students. If there are
9
9
9
teachers to choose from, and
9
9
9
students, how many different ways could the committee be made?
\newline
Answer:
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In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If
12
12
12
boys and
6
6
6
girls are competing, how many different ways could the six medals possibly be given out?
\newline
Answer:
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In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If
6
6
6
boys and
15
15
15
girls are competing, how many different ways could the six medals possibly be given out?
\newline
Answer:
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A committee must be formed with
5
5
5
teachers and
4
4
4
students. If there are
8
8
8
teachers to choose from, and
15
15
15
students, how many different ways could the committee be made?
\newline
Answer:
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A committee must be formed with
3
3
3
teachers and
6
6
6
students. If there are
11
11
11
teachers to choose from, and
16
16
16
students, how many different ways could the committee be made?
\newline
Answer:
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A committee must be formed with
4
4
4
teachers and
6
6
6
students. If there are
6
6
6
teachers to choose from, and
14
14
14
students, how many different ways could the committee be made?
\newline
Answer:
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A committee must be formed with
4
4
4
teachers and
3
3
3
students. If there are
9
9
9
teachers to choose from, and
13
13
13
students, how many different ways could the committee be made?
\newline
Answer:
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A committee must be formed with
3
3
3
teachers and
6
6
6
students. If there are
8
8
8
teachers to choose from, and
17
17
17
students, how many different ways could the committee be made?
\newline
Answer:
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A committee must be formed with
4
4
4
teachers and
4
4
4
students. If there are
7
7
7
teachers to choose from, and
9
9
9
students, how many different ways could the committee be made?
\newline
Answer:
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Amari has
8
8
8
paint colors available, and he wants to mix
3
3
3
of them to create a new color.
\newline
How many different sets of
3
3
3
colors can Amari choose?
\newline
□
\square
□
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There are
9
9
9
different actors auditioning for the roles of Larry, Curly and Moe. How many ways could the roles be cast?
\newline
Answer:
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Students are making lemonade from a powdered lemon drink mix. Carlos mixes
2
2
2
cups of water and
3
3
3
teaspoons of powdered lemon mix. Sophie mixes
2
2
2
cups of water and
5
5
5
teaspoons of powdered lemon mix. Whose mix will be more lemony?
\newline
Carlos's mix will be more lemony.
\newline
Sophie's mix will be more lemony.
\newline
The two mixes will be equally lemony.
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A sporting goods store offers
3
3
3
different types of bicycles (mountain, racing, and BMX) and
3
3
3
different wheel sizes (
20
20
20
in,
22
22
22
in, and
24
24
24
in). How many bicycle choices does the store offer?
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Betty's Bakery calculates the total price
d
d
d
in dollars for
c
c
c
cupcakes using the equation
d
=
2
c
d=2 c
d
=
2
c
.
\newline
What does
2
2
2
mean in this situation?
\newline
Choose
1
1
1
answer:
\newline
(A) The bakery charges
$
2
\$ 2
$2
for each cupcake.
\newline
(B) The bakery sells
2
2
2
cupcakes for a dollar.
\newline
(C) The bakery sells
2
2
2
types of cupcakes.
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A baseball team has three different pitchers. Randy allowed
2
2
2
runs and pitched
3
3
3
innings. Felix allowed
4
4
4
runs and pitched
5
5
5
innings. Johan allowed
5
5
5
runs and pitched
7
7
7
innings.
\newline
Which pitcher has the lowest number of runs allowed per inning?
\newline
Choose
1
1
1
answer:
\newline
(A) Randy
\newline
(B) Felix
\newline
(C) Johan
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Three different golfers played a different number of holes today. Shanika played
9
9
9
holes and had a total of
43
43
43
strokes. Alicia played
18
18
18
holes and had a total of
79
79
79
strokes. Rickie played
27
27
27
holes and had a total of
123
123
123
strokes.
\newline
Which golfer had the lowest number of strokes per hole?
\newline
Choose
1
1
1
answer:
\newline
(A) Shanika
\newline
(B) Alicia
\newline
(C) Rickie
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Liliana used
4
4
4
dark power crystals to raise
14
14
14
zombie soldiers. She wants to know how many zombie soldiers
(
z
)
(z)
(
z
)
she can raise with
10
10
10
dark power crystals.
\newline
How many zombie soldiers can Liliana raise with
10
10
10
power crystals?
\newline
zombie soldiers
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Woo Jin is solving the following equation for
x
x
x
.
\newline
7
−
4
x
=
x
+
3
7-4 x=\sqrt{x+3}
7
−
4
x
=
x
+
3
\newline
His first few steps are given below.
\newline
(
7
−
4
x
)
2
=
(
x
+
3
)
2
49
−
56
x
+
16
x
2
=
x
+
3
\begin{aligned} (7-4 x)^{2} & =(\sqrt{x+3})^{2} \\ 49-56 x+16 x^{2} & =x+3 \end{aligned}
(
7
−
4
x
)
2
49
−
56
x
+
16
x
2
=
(
x
+
3
)
2
=
x
+
3
\newline
Is it necessary for Woo Jin to check his answers for extraneous solutions?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B)
N
o
\mathrm{No}
No
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Jonas is planning out his route for an upcoming race. He uses negative numbers to represent points before the finish line and positive numbers to represent points after the finish line.
\newline
On Jonas's map, there is a bridge at
−
91
-91
−
91
meters, and a restaurant is at
14
14
14
meters.
\newline
What does
0
0
0
meters represent?
\newline
Choose
1
1
1
answer:
\newline
(A) The bridge
\newline
(B) The restaurant
\newline
(C) The finish line
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Four college roommates go to the doctor for their annual check up. All of the roommates compare their weights to the previous year.
\newline
Bao lost
4
k
g
4 \mathrm{~kg}
4
kg
over the year.
\newline
Shanta lost
2
k
g
2 \mathrm{~kg}
2
kg
over the year.
\newline
Ruth gained
3
k
g
3 \mathrm{~kg}
3
kg
over the year.
\newline
Morty gained
2
k
g
2 \mathrm{~kg}
2
kg
over the year.
\newline
Which roommate had the greatest change in weight?
\newline
Choose
1
1
1
answer:
\newline
(A) Bao
\newline
(B) Shanta
\newline
(C) Ruth
\newline
(D) Morty
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Simon is creating a flower arrangement. A client asked him to select
4
4
4
of the
7
7
7
available flower options to create the arrangement.
\newline
How many different groups of
4
4
4
flowers can Simon choose?
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A club is going to send
4
4
4
of its
10
10
10
members to represent the club at a conference.
\newline
How many different groups of
4
4
4
members can they send?
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Amari has
8
8
8
paint colors available, and he wants to mix
3
3
3
of them to create a new color.
\newline
How many different sets of
3
3
3
colors can Amari choose?
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Elena is managing a construction project. She has
7
7
7
workers available to work on a given day, and she needs to select
5
5
5
of them.
\newline
How many different sets of
5
5
5
workers can Elena choose?
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Luis is packing a bag for vacation. He has
9
9
9
unique shirts, but he can only fit
5
5
5
in his bag.
\newline
How many different groups of
5
5
5
shirts can he take?
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When a customer buys a familysized meal at certain restaurant, they get to choose
3
3
3
side dishes from
9
9
9
options. Suppose a customer is going to choose
3
3
3
different side dishes.
\newline
How many groups of
3
3
3
different side dishes are possible?
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Karla is creating a survey with
6
6
6
questions. She suspects that the order of the questions may influence the responses, so she wants to create multiple versions of the survey with the same
6
6
6
questions in different orders.
\newline
How many unique ways are there to arrange the questions?
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Mateo is playing a word game where he's trying to make
4
4
4
-letter words by rearranging the letters in the word IRON.
\newline
How many unique ways are there to arrange the letters in the word IRON?
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Amara needs to create a special tasting menu at her restaurant. She needs to select
4
4
4
dishes from
7
7
7
available dishes and put them in a tasty sequence.
\newline
How many unique ways are there to arrange
4
4
4
of the
7
7
7
dishes?
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A swimming coach needs to choose a team for a relay race. The coach must select
4
4
4
of
6
6
6
available swimmers and put them in a strategic sequence.
\newline
How many unique ways are there to arrange
4
4
4
of the
6
6
6
swimmers?
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Seven runners are competing in a race where
3
3
3
of them will earn medals for finishing first, second, and third.
\newline
How many unique ways are there to arrange
3
3
3
of the
7
7
7
runners in first, second, and third place?
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Yuki's summer job at the frozen yogurt shop paid
$
324
\$ 324
$324
in her first
3
3
3
days on the job. She got paid the same hourly rate every day, and she worked
8
8
8
hours per day. How many dollars did Yuki make per hour?
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Jocelyn enjoys building robots and painting pictures. It takes her a constant amount of time to build every robot, and it takes her a constant amount of time to paint every picture. She has
15
15
15
hours to build robots and paint pictures.
\newline
In the following inequality,
R
R
R
represents the number of robots Jocelyn can build and
P
P
P
represents the number of paintings she can create over that time period:
\newline
2
R
+
5
P
≤
15
2 R+5 P \leq 15
2
R
+
5
P
≤
15
\newline
Jocelyn wants to build
3
3
3
robots. How many paintings at most can she create in the time that remains?
\newline
Choose
1
1
1
answer:
\newline
(A) Jocelyn can create at most
0
0
0
paintings.
\newline
(B) Jocelyn can create at most
1
1
1
painting.
\newline
(C) Jocelyn can create at most
2
2
2
paintings.
\newline
(D) Jocelyn can create at most
3
3
3
paintings.
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In Sakura's garden, for every
5
5
5
red flowers, there are
10
10
10
yellow flowers. There are a total of
75
75
75
yellow and red flowers in her garden.
\newline
How many red flowers are in Sakura's garden?
\newline
red flowers
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A fruit basket is filled with
8
8
8
bananas,
3
3
3
oranges,
5
5
5
apples, and
6
6
6
kiwis.
\newline
Complete the ratio.
\newline
For every
3
3
3
kiwis, there are
4
4
4
_____ (Select a fruit).
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