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Math Problems
Algebra 1
Modeling with linear inequalities
Pierre wants to make tables and chairs. He has a total of
220
220
220
wooden boards and
760
760
760
nails.
\newline
13
T
+
8
C
≤
220
13T+8C \leq 220
13
T
+
8
C
≤
220
represents the number of tables
T
T
T
and chairs
C
C
C
he can make with
220
220
220
wooden boards.
\newline
48
T
+
37
C
≤
760
48T+37C \leq 760
48
T
+
37
C
≤
760
represents the number of tables and chairs he can make with
760
760
760
nails.
\newline
Does Pierre have enough boards and nails to make
9
9
9
tables and
5
5
5
chairs?
\newline
Choose
1
1
1
answer:
\newline
(A) Pierre has enough boards and nails.
\newline
(B) Pierre has enough boards but not enough nails.
\newline
(C) Pierre has enough nails but not enough boards.
\newline
(D) Pierre has neither enough boards nor enough nails.
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Caissa can download a maximum of
1000
MB
1000\,\text{MB}
1000
MB
of songs or movies to her smartphone each month. The file size of each movie is
85
MB
85\,\text{MB}
85
MB
, and the file size of each song is
4
MB
4\,\text{MB}
4
MB
. Write an inequality that represents the number of movies
(
M
)
(M)
(
M
)
and songs
(
S
)
(S)
(
S
)
that Caissa can download each month.
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Ezra enjoys gardening.
\newline
Let
S
S
S
represent the number of sunflower plants and
L
L
L
represent the number of lily plants Ezra's water supply can water.
\newline
0.7
S
+
0.5
L
≤
11
0.7S + 0.5L \leq 11
0.7
S
+
0.5
L
≤
11
\newline
Ezra waters
10
10
10
lily plants. How many sunflower plants can he water at most with the remaining amount of water?
\newline
Choose
1
1
1
answer:
\newline
(A) Ezra can water
7
7
7
sunflower plants at most.
\newline
(B) Ezra can water
8
8
8
sunflower plants at most.
\newline
(C) Ezra can water
10
10
10
sunflower plants at most.
\newline
(D) Ezra can water
11
11
11
sunflower plants at most.
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Nathaniel builds birds and birdhouses using Lego blocks.
\newline
Let
B
B
B
represent the number of birds and
\newline
H
H
H
represent the number of birdhouses that Nathaniel can build with his Lego blocks.
\newline
43
B
+
215
H
≤
3000
43B + 215H \leq 3000
43
B
+
215
H
≤
3000
\newline
Nathaniel wants to build
50
50
50
birds using Lego blocks. How many birdhouses can he build at most with the remaining Lego blocks?
\newline
Choose
1
1
1
answer:
\newline
(A) Nathaniel can build at most
1
1
1
birdhouse.
\newline
(B) Nathaniel can build at most
2
2
2
birdhouses.
\newline
(C) Nathaniel can build at most
3
3
3
birdhouses.
\newline
(D) Nathaniel can build at most
4
4
4
birdhouses.
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Fleur wants to make tables and chairs. She has a total of
150
150
150
wooden boards and
330
330
330
nails.
\newline
17
T
+
6
C
≤
150
17T+6C \leq 150
17
T
+
6
C
≤
150
represents the number of tables
T
T
T
and chairs
C
C
C
she can make with
150
150
150
wooden boards.
\newline
34
T
+
27
C
≤
330
34T+27C \leq 330
34
T
+
27
C
≤
330
represents the number of tables and chairs she can make with
330
330
330
nails.
\newline
Does Fleur have enough boards and nails to make
3
3
3
tables and
9
9
9
chairs?
\newline
Choose
1
1
1
answer:
\newline
(A) Fleur has enough boards and nails.
\newline
(B) Fleur has enough boards but not enough nails.
\newline
(C) Fleur has enough nails but not enough boards.
\newline
(D) Fleur has neither enough boards nor enough nails.
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Michelle has a maximum of
4500
4500
4500
milliliters (ml) of water for her plants today. Each basil plant requires
350
ml
350\text{ml}
350
ml
of water, and each fennel plant requires
525
ml
525\text{ml}
525
ml
of water.
\newline
Write an inequality that represents the number of basil plants
(
B
)
(B)
(
B
)
and fennel plants
(
F
)
(F)
(
F
)
Michelle can water today.
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In order to win a quiz contest, Olga must score more than
400
400
400
points. She earns
12
12
12
points for each right answer, and loses
4
4
4
points for each wrong answer.
\newline
Write an inequality that represents the number of right answers
(
R
)
(R)
(
R
)
and wrong answers
(
W
)
(W)
(
W
)
Olga can give to win the contest.
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Fabiano wants to score at least
6.5
6.5
6.5
points in a major chess tournament. He scores
1
1
1
point for each game that he wins, and he scores
0.5
0.5
0.5
points for each game that ends in a draw.
\newline
Write an inequality that represents the number of games Fabiano should win
\newline
(
W
)
(W)
(
W
)
and draw
\newline
(
D
)
(D)
(
D
)
to achieve his goal.
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Sania plays a game in which she pops balloons and slices fruits.
\newline
Let
\newline
B
B
B
represent the number of points Sania must score by popping balloons and
\newline
F
F
F
represent the number of points she must score by slicing fruits in order to win the game.
\newline
7
B
+
13
F
>
650
7B + 13F > 650
7
B
+
13
F
>
650
\newline
Sania pops
30
30
30
balloons in the game. What is the least number of fruits she must slice to reach her goal?
\newline
Choose
1
1
1
answer:
\newline
(A) Sania must slice at least
13
13
13
fruits.
\newline
(B) Sania must slice at least
30
30
30
fruits.
\newline
(C) Sania must slice at least
33
33
33
fruits.
\newline
(D) Sania must slice at least
34
34
34
fruits.
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Alfred wants to waste less than
175
175
175
gallons of water this week. Every day that he waters the lawn, he wastes
59
59
59
gallons of water. Every day that he washes his car, he wastes
28
28
28
gallons of water.
\newline
Write an inequality that represents the number of days Alfred should water the lawn
\newline
(L) and wash his car
\newline
(C) to achieve his goal.
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Wang Hao wants to spend at most
(
15
(15
(
15
on dairy products. Each liter of goat milk costs
)
2.40
)2.40
)
2.40
, and each liter of cow's milk costs
$
1.20
\$1.20
$1.20
. Write an inequality that represents the number of liters of goat milk
G
G
G
and cow's milk
C
C
C
Wang Hao can buy on his budget.
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Wahab wants to donate at least
$
6000
\$6000
$6000
in books and pairs of shoes.
\newline
Let
B
B
B
represent the number of books and
S
S
S
represent the number of pairs of shoes that Wahab must donate to achieve his goal.
\newline
20
B
+
50
S
≥
6000
20B + 50S \geq 6000
20
B
+
50
S
≥
6000
\newline
Wahab donates
100
100
100
pairs of shoes. What is the least number of books he should donate to achieve his goal?
\newline
Choose
1
1
1
answer:
\newline
(A) Wahab should donate at least
20
20
20
books.
\newline
(B) Wahab should donate at least
50
50
50
books.
\newline
(C) Wahab should donate at least
80
80
80
books.
\newline
(D) Wahab should donate at least
100
100
100
books.
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Gulnaz plans to use less than
26
26
26
eggs while baking. She uses
5
5
5
eggs for each cake that she bakes, and
3
3
3
eggs for each quiche that she bakes.
\newline
Write an inequality that represents the number of cakes
(
C
)
(C)
(
C
)
and quiches
(
Q
)
(Q)
(
Q
)
Gulnaz can bake according to her plan.
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Horace is a professional hair stylist.
\newline
Let
C
C
C
represent the number of child haircuts and
A
A
A
represent the number of adult haircuts that Horace can give within
7
7
7
hours.
\newline
0.75
C
+
1.25
A
≤
7
0.75C + 1.25A \leq 7
0.75
C
+
1.25
A
≤
7
\newline
Horace gave
5
5
5
child haircuts. How many adult haircuts at most can he give with the remaining time?
\newline
Choose
1
1
1
answer:
\newline
(A) Horace can give at most
1
1
1
adult haircut.
\newline
(B) Horace can give at most
2
2
2
adult haircuts.
\newline
(C) Horace can give at most
3
3
3
adult haircuts.
\newline
(D) Horace can give at most
5
5
5
adult haircuts.
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A robot is expected to filter pollution out of at least
350
350
350
liters of air and water. It filters air at the rate of
50
50
50
liters per minute, and it filters water at the rate of
20
20
20
liters per minute.
\newline
Write an inequality that represents the number of minutes the robot should filter air
(
A
)
(A)
(
A
)
and water
(
W
)
(W)
(
W
)
to meet this expectation.
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Hyun Yong wants to donate more than
(
5000
(5000
(
5000
in laptops and bicycles. Each laptop that he donates is worth
)
200
)200
)
200
, and each bicycle that he donates is worth
$
100
\$100
$100
. Write an inequality that represents the number of laptops
L
L
L
and bicycles
B
B
B
that Hyun Yong should donate to achieve his goal.
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Noor wants to spend less than
(
20
(20
(
20
on condiments. Each kilogram of salt costs
)
1.50
)1.50
)
1.50
, and each kilogram of pepper costs
$
2.50
\$2.50
$2.50
. Write an inequality that represents the number of kilograms of salt
S
S
S
and pepper
P
P
P
Noor can buy on her budget.
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Vivek has a maximum of
49
49
49
seconds to chop tomatoes and zucchinis. It takes him
6
6
6
seconds to chop each tomato, and
4
4
4
seconds to chop each zucchini.
\newline
Write an inequality that represents the number of tomatoes
\newline
(
T
)
(T)
(
T
)
and zucchinis
\newline
(
Z
)
(Z)
(
Z
)
Vivek can chop within this time limit.
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Miyoko's goal is to earn more than
(
950
(950
(
950
this week. She earns
)
250
)250
)
250
for every day she works as a cryptographer, and earns
$
180
\$180
$180
for every day she works as a geologist.
\newline
Write an inequality that represents the number of days Miyoko should work as a cryptographer
C
C
C
and as a geologist
G
G
G
to achieve her goal.
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Eldar cooks lasagna and spaghetti using pesto sauce.
\newline
Let
\newline
L
L
L
represent the number of batches of lasagna and
\newline
S
S
S
represent the number of batches of spaghetti that Eldar can cook with the amount of pesto sauce he has.
\newline
0.9
L
+
0.3
S
≤
6
0.9L + 0.3S \leq 6
0.9
L
+
0.3
S
≤
6
\newline
Eldar cooks
4
4
4
batches of spaghetti. How many batches of lasagna can he cook at most with the remaining pesto sauce?
\newline
Choose
1
1
1
answer:
\newline
(A) Eldar can cook
3
3
3
batches of lasagna at most.
\newline
(B) Eldar can cook
4
4
4
batches of lasagna at most.
\newline
(C) Eldar can cook
5
5
5
batches of lasagna at most.
\newline
(D) Eldar can cook
6
6
6
batches of lasagna at most.
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Eliana takes photos and videos on her phone.
\newline
Let
P
P
P
represent the number of photos and
V
V
V
represent the number of videos that Eliana can take using her storage space.
\newline
15
P
+
70
V
<
400
15P + 70V < 400
15
P
+
70
V
<
400
\newline
Eliana wants to take
12
12
12
photos. How many videos at most can she take with the remaining storage space?
\newline
Choose
1
1
1
answer:
\newline
(A) Eliana can take at most
3
3
3
videos.
\newline
(B) Eliana can take at most
4
4
4
videos.
\newline
(C) Eliana can take at most
12
12
12
videos.
\newline
(D) Eliana can take at most
15
15
15
videos.
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A colony of flowers is pollinated by hummingbirds and sunbirds.
\newline
Let
\newline
H
H
H
represent the number of hummingbirds and
\newline
S
S
S
represent the number of sunbirds that must pollinate the colony so it can survive until next year.
\newline
6
H
+
4
S
>
74
6H+4S > 74
6
H
+
4
S
>
74
\newline
This year,
8
8
8
hummingbirds pollinated the colony. What is the least number of sunbirds that must pollinate the colony to ensure that it will survive until next year?
\newline
Choose
1
1
1
answer:
\newline
(A) At least
4
4
4
sunbirds must pollinate the colony.
\newline
(B) At least
6
6
6
sunbirds must pollinate the colony.
\newline
(C) At least
7
7
7
sunbirds must pollinate the colony.
\newline
(D) At least
8
8
8
sunbirds must pollinate the colony.
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