Welcome to **AMBiPi (Amans Maths Blogs)**. In this article, you will get * SAT 2022 Practice Test System of Linear Inequalities Word Problems | SAT Online Tutor AMBiPi*.

### SAT 2022 Math Multiple Choice Practice Questions

#### System of Linear inequalities Word Problems Multiple Choice Questions with Answer Keys

**SAT Practice Test Question No 1:**

In order to keep a malfunctioning satellite from falling into the earth, space agency officials decide to use a powerful rocket. At the time the rocket is attached, the satellite will be traveling with an initial velocity, υ0 , and for every second that the rocket fires, it will add approximately 180 meters per second (m/s) to this velocity. In order to ensure safety on earth, the velocity must be increased to at least 3,800 m/s Also, the rocket can fire for no more than 4 seconds. For the initial velocity of the satellite, v_{0}, which of the following systems of inequalities best models this situation, where t is time, in seconds, after the rocket is first fired?

**Option A** : v_{o} + 180t ≥ 3800 and t ≤ 4

**Option B** : v_{o} + 180t ≥ 3800 and 180t ≤ 4

**Option C** : v_{o} + 3800 ≤ 180t and t ≤ 4

**Option D** : v_{o} + 3800 ≤ 180t and 180t ≤ 4

**Show/Hide Answer Key**

**Option A : v _{o} + 180t ≥ 3800 and t ≤ 4**

**SAT Practice Test Question No 2:**

Vijay needs to take a taxi, which costs a flat fee of 3 dollars, plus an additional 4 dollars per mile. If Vijay has a dollars with him, which inequality shows the number of miles, m, he can afford to travel in the taxi?

**Option A** : 0 ≤ m ≤ 4a + 3

**Option B** : 0 ≤ m ≤ a/4 – 3/4

**Option C** : 4a – 3 ≤ m

**Option D** : None of these

**Show/Hide Answer Key**

**Option B : 0 ≤ m ≤ a/4 – 3/4**

**SAT Practice Test Question No 3:**

In order to bring his business to the next level, Christov wants to gain at least 2,000 followers on a popular social media platform. From his own personal account, he knows that each original post gains him approximately 3 new followers and every 5 reposts gains about 1. Which of the following inequalities represents the numbers of posts, P, and reposts, R, Christov needs to reach his goal of gaining 2,000 followers?

**Option A** : 3P + 0.2R ≥ 2000

**Option B** : 3P + 5R ≤ 2000

**Option C** : 1P + 5R ≥ 2000

**Option D** : 0.2P + 5R ≤ 2000

**Show/Hide Answer Key**

**Option A : 3P + 0.2R ≥ 2000**

**SAT Practice Test Question No 4:**

A company sells candy in jars that each have a volume of 3 cups. Each jar is filled above a certain line, guaranteeing that it has more than 8/3 cups of candy. Which of the following graphs shows the possible volumes of candy, c, in cups, a customer may have, given that they bought j jars of candy?

**Option A** :

**Option B** :

**Option C** :

**Option D** :

**Show/Hide Answer Key**

**Option B : **

**SAT Practice Test Question No 5:**

Prachi needs between 240 and 260 total feet of fence panels. The home improvement store has 24 short (6-foot) fence panels and 28 long (8-foot) fence panels in stock. Which of the following combinations of fence panels could she buy?

**Option A** : 6 short fence panels and 26 long fence panels

**Option B** : 8 short fence panels and 23 long fence panels

**Option C** : 27 short fence panels and 12 long fence panels

**Option D** : 30 short fence panels and 10 long fence panels

**Show/Hide Answer Key**

**Option A : 6 short fence panels and 26 long fence panels**

**SAT Practice Test Question No 6:**

Priyanka’s car gets a maximum of 35 miles per gallon. According to a particular convention, the “wear” on a vehicle is at least 15/4 times the total number of miles driven plus the total number of gallons used. For Priyanka’s car, let m be the total number of miles driven, let g be the total number of gallons used, and let w be the “wear”. Which of the following systems of inequalities correctly represents these relationships?

**Option A** : w – g ≥ 15/4 and m ≤ 35g

**Option B** : w – g < 15/4 and m ≥ 35g

**Option C** : w – g ≥ 15/4 and 35m ≤ g

**Option D** : w – g < 15/4 and 35m ≥ g

**Show/Hide Answer Key**

**Option A : w – g ≥ 15/4 and m ≤ 35g**

**SAT Practice Test Question No 7:**

K = (4.14 × 10^{-15})v – φ

In night vision goggles, light rays cause electrons to be projected from a metal surface. The above equation relates the kinetic energy in electron volts (eV), K, of emitted electrons to the frequency in hertz, v , of incident light rays and the work function, φ, in eV, of the metallic surface?

In a particular set of night vision goggles, the electrons emitted must have a kinetic energy of at least 2.46 eV. If the frequency of incoming light rays is less than 14 9.60 ⋅10 hertz , which of the following systems of inequalities best models the relationship between the work function, φ , and the light source frequency, v ?

**Option A** : v > 9.60 × 10^{14 }and φ ≤ (4.14 × 10^{-15})v – 2.46

**Option B** : v < 9.60 × 10^{14 }and φ ≤ (4.14 × 10^{-15})v – 2.46

**Option C** : v > 9.60 × 10^{14 }and φ ≥ (4.14 × 10^{-15})v – 2.46

**Option D** : v < 9.60 × 10^{14 }and φ ≤ (4.14 × 10^{-15})v – 2.46

**Show/Hide Answer Key**

**Option B : v < 9.60 × 10 ^{14 }and φ ≤ (4.14 × 10^{-15})v – 2.46**

**SAT Practice Test Question No 8:**

Paper Scraper, Inc, a mobile paper shredding and recycling company, receives $0.39 for each pound of paper they shred, but it costs them approximately $1.38 per mile to operate their truck. Any job that requires less than 200 miles of travel, and also nets at least $500 profit, qualifies for free delivery. Of the following, which combination of size in pounds and distance in miles would qualify for free delivery?

**Option A** : Paul has 1100 pounds of paper that requires 3 miles of travel.

**Option B** : Li Min has 1500 pounds of paper that requires 107 miles of travel.

**Option C** : Amira has 1800 pounds of paper that requires 94 miles of travel.

**Option D** : Jarles has 3500 pounds of paper that requires 225 miles of travel.

**Show/Hide Answer Key**

**Option C : Amira has 1800 pounds of paper that requires 94 miles of travel.**

**SAT Practice Test Question No 9:**

A technology store sells tablets and computers. In January they sell over 300 items, and more of those sales are tablets than computers. In February they sell exactly 100 tablets and 20 computers. The graph at left shows two equations related to this problem, where t is the total tablet sales (in January and February combined), and c is the total computer sales. Which of the following combinations could be the technology store’s total sales?

**Option A** : 240 tablets and 100 computers

**Option B** : 360 tablets and 180 computers

**Option C** : 240 tablets and 260 computers

**Option D** : 120 tablets and 180 computers

**Show/Hide Answer Key**

**Option B : 360 tablets and 180 computers**

**SAT Practice Test Question No 10:**

Elena is designing a paint can with thickness t millimeters and height h centimeters. She calculates that the thickness of the can in milimeters must be at least 0.1 times the height of the can in centimeters in order to withstand pressure. Due to cost constraints, the cost of material used, (0.2+t+0.5h) cents, must be at most 12.2 cents. Which of the following systems of inequalities best models the relationship between height and thickness described above?

**Option A** : t ≤ 12 – h/2 and 10t ≥ h

**Option B** : t ≤ 12 – h/2 and t ≥ 10h

**Option C** : t ≥ 12 – h/2 and 10t ≥ h

**Option D** : t ≥ 12 – h/2 and t ≥ 10h

**Show/Hide Answer Key**

**Option A: t ≤ 12 – h/2 and 10t ≥ h**

**SAT Practice Test Question No 11:**

Anna is considering three insurance options for her business, shown in the table below.

She wants the total cost, (c + d), to be at most $2,000. She also wants the benefit, which is 9090 percent of (10c + d), to be at least $12,400. Which of the following option selections would fit Anna’s plan?

**Option A** : Option 11 and 22 work

**Option B** : Only option 22 works

**Option C** : Only option 33 works

**Option D** : None of the above

**Show/Hide Answer Key**

**Option A : Option 11 and 22 work**

**SAT Practice Test Question No 12:**

Aaron is purchasing party hats and fake mustaches for an end of the school year party. He can spend at most $30. Fake mustaches cost $3 each, and party hats cost $2 each. If he must purchase a combination of at least 15 mustaches and party hats, which of the following systems of inequalities best models the relationship between the number of mustaches, m, and party hats, p, described above?

**Option A** : m + p ≥ 15 and 3m + 2p ≤ 30

**Option B** : m + p ≤ 15 and 3m + 2p ≥ 30

**Option C** : 3m + 2p ≥ 15 and m + p ≤ 30

**Option D** : 3m + 2p ≤ 15 and m + p ≥ 30

**Show/Hide Answer Key**

**Option A : m + p ≥ 15 and 3m + 2p ≤ 30**

**SAT Practice Test Question No 13:**

Arturo goes to his neighborhood store to purchase almonds and walnuts for an old family recipe. One pound of almonds costs $2, and one pound of walnuts costs $4. Arturo can spend at most $18 on almonds and walnuts. The graph at left, in the wa-plane, relates the number of pounds, w, of walnuts to the number of pounds, a, of almonds which Arturo can purchase and have enough for his recipe. Which of the following amounts of walnuts and almonds can he purchase?

**Option A** : 2 pounds of walnuts and 11 pound of almonds

**Option B** : 33 pounds of walnuts and 77 pound of almonds

**Option C** : 44 pounds of walnuts and 22 pound of almonds

**Option D** : 22 pounds of walnuts and 44 pound of almonds

**Show/Hide Answer Key**

**Option D : 22 pounds of walnuts and 44 pound of almonds**

**SAT Practice Test Question No 14:**

q ≤ 4000 – 5p

p ≥ 200

q ≥ 0

In a standard economic supply and demand graph, consumer surplus is defined as the area greater than or equal to the equilibrium price of a good and less than or equal to the demand line. The system of linear inequalities written and graphed at left, where p represents price and q represents the quantity of units that consumers will demand, shows the consumer surplus area for a tablet computer that recently entered the U.S. marketplace. What is the maximum quantity of the tablet that consumers will demand and still have it remain in the consumer surplus area of the graph?

**Option A** : 200

**Option B** : 800

**Option C** : 2800

**Option D** : 3000

**Show/Hide Answer Key**

**Option D : 3000**

**SAT Practice Test Question No 15:**

Julia mows lawns in the summer for $15 per lawn. It costs Julia between $2 and $4 to mow 1 lawn. If l represents the number of lawns Julia mows, which graph correctly shades the possible values of Julia’s net earnings, d, in dollars?

**Option A** :

**Option B** :

**Option C** :

**Option D** :

**Show/Hide Answer Key**

**Option B : **

### SAT 2022 Math Grid-in Practice Questions

#### System of Linear Inequalities Word Problems Grid-in Choice Questions with Answer Keys

**SAT Practice Test Question No 16:**

In tennis, a player must win 6 games in order to win a set. However, winning 6 games does not guarantee that the player will win the set. If g is the number of games the player won and s is the number of sets the player won, write an inequality that relates g and s?

**Show/Hide Answer Key**

**Correct Answer : 6s ≤ g**

**SAT Practice Test Question No 17:**

Kaylee and Mariana are runners. In 1 hour, Kaylee can run around the track 48.5 times and Mariana can run around the park trail 4 times. Let t be the length of the track and p be the length of the park trail, both in meters. If Kaylee is the faster runner, write an inequality that relates p and t?

**Show/Hide Answer Key**

**Correct Answer : 4p < 48.5t**

**SAT Practice Test Question No 18:**

Roberto plans to start a new job. In preparation, he decides that he should spend no more than 30 hours per week on the job and homework combined. If Roberto wants to have at least 2 homework hours for every 1 hour at his job, what is the maximum number of hours that he should spend at his job each week?

**Show/Hide Answer Key**

**Correct Answer : 10 hours**

**SAT Practice Test Question No 19:**

A tennis club is organizing group lessons. The club supplies 40 new balls for each player which cost $1 each. Each player pays $300 for the lessons. The club must pay each instructor $1,000 for conducting the lessons, and there must be at least 1 instructor for every 6 players. Which amount of players and instructors meets these requirements and still gives the club a net profit?

**Show/Hide Answer Key**

**Correct Answer : 16 players and 3 instructors**

**SAT Practice Test Question No 20:**

A business analyst is deciding the amount of time allotted to each employee for meetings and training. He wants the sum of meeting and training time to be no more than 16 hours per month. Also, there should be at least one training hour for every two meeting hours. Finally, there should be at least 2 meeting hours per month to discuss short-term goals. What is the difference between the maximum and minimum number of monthly training hours that could be allotted to an employee?

**Show/Hide Answer Key**

**Correct Answer : 13 hours**