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

### SAT 2022 Math Multiple Choice Practice Questions

#### Linear Inequalities Word Problems Multiple Choice Questions with Answer Keys

**SAT Math Question No 1:**

The following function gives the amount of money owed on a short term loan after t weeks.

A(t) = 100×1.25^{1/2}.

Which numerical expression best approximates the annual interest rate, excluding any late fees? (1 year = 52 weeks)

**Option A** : 1 – 0.25^{26}

**Option B** : 0.25^{26} – 1

**Option C** : 26 × 0.25

**Option D** : 26 × 1.25

**Show/Hide Answer Key**

**Option B : 0.25 ^{26} – 1**

**SAT Math Question No 2:**

More than 450 students traveled to a state park for a field trip. The school allowed 6 students to travel by car, and the rest traveled on 11 buses, each of which held the same number of students. If there were s students in each bus, which inequality best represents this situation?

**Option A** : 11s + 6 > 450

**Option B** : 11s + 6 < 450

**Option C** : 6s + 11 > 450

**Option D** : 6s + 11 < 450

**Show/Hide Answer Key**

**Option A : 11s + 6 > 450**

**SAT Math Question No 3:**

A barber charges $12 for a haircut. His operating expenses are, on average, $37 per day. He calculates his profit by subtracting his operating costs from the money he earns from the haircuts he gives. In a given day, the barber expects to make a profit of at least $86. If the barber gives h haircuts in a day, which inequality best models this situation?

**Option A** : 12h – 37 ≥ 86

**Option B** : 12(h – 37) ≥ 86

**Option C** : 12h + 37 ≥ 86

**Option D** : 12(h + 37) ≥ 86

**Show/Hide Answer Key**

**Option A : 12h – 37 ≥ 86**

**SAT Math Question No 4:**

A distributor ships DVDs to several stores. The shipping boxes contain several DVDs (in their cases) plus a layer of adding at each end of the box. The DVD cases and layers of padding can be arranged neatly inside each box. Each DVD case is 14 mm (millimeters) thick, each layer of padding is 10 mm thick, and the length of the interior of the box is 132 mm. If d represents the number of DVDs that the distributor can fit into one box with two layers of padding, which of the following inequalities best models the situation?

**Option A** : 10d + 14 ≤ 132

**Option B** : 14d + 20 ≤ 132

**Option C** : 20d + 14 ≤ 132

**Option D** : 14d + 10 ≤ 132

**Show/Hide Answer Key**

**Option B : 14d + 20 ≤ 132**

**SAT Math Question No 5:**

To rent a car for one week, a car rental company charges a $200 base price as well as $0.45 per mile. Jennifer will rent a vehicle at this company, but she has a $275 budget. Which of the following is a possible number of miles that Jennifer can drive without exceeding her budget?

**Option A** : 166 miles

**Option B** : 167 miles

**Option C** : 168 miles

**Option D** : 169 miles

**Show/Hide Answer Key**

**Option A : 166 miles**

**SAT Math Question No 6:**

Woo-Jin would like to bring several books from his favorite series in his backpack. The backpack can hold up to a depth of 10 1/2 inches of materials. Woo-Jin’s laptop and a notebook fill a total of 3 inches of that depth. Each book would fill 1.5 inches of the depth of the backpack. Only one stack of books can fit the height and width of the backpack. If x represents the number of books that Woo-Jin could carry in his backpack, which of the following inequalities best models the situation described above?

**Option A** : 3 + 1.5x < 10.5

**Option B** : 3 + 1.5x ≤ 10.5

**Option C** : 3x + 1.5 < 10.5

**Option D** : 3x + 1.5 ≤ 10.5

**Show/Hide Answer Key**

**Option B : 3 + 1.5x ≤ 10.5**

**SAT Math Question No 7:**

In the year 2000, the average American consumed 8.3 gallons of whole milk per year. This amount has been decreasing by 0.3 gallons per year. Which inequality can be used to find the number of years, t, since 2000 when whole milk consumption was greater than 6.0 gallons per person per year?

**Option A** : 8.3 – 0.3t > 6.0

**Option B** : 8.3 – 0.3(t – 2000) > 6.0

**Option C** : 8.3 – 0.3t < 6.0

**Option D** : 8.3 – 0.3(t – 2000) < 6.0

**Show/Hide Answer Key**

**Option A : 8.3 – 0.3t > 6.0**

**SAT Math Question No 8:**

An amusement center charges a $45 flat fee for any birthday party plus $3.50 for each guest after the first one. Josiah wants to spend no more than $200 for his birthday party. If there are x guests, which of the following inequalities best models the situation above?

**Option A** : 45 + 3.50x ≤ 200

**Option B** : 45 + 3.50(x – 1) ≤ 200

**Option C** : 45x + 3.50 ≤ 200

**Option D** : 45(x – 1) + 3.50 ≤ 200

**Show/Hide Answer Key**

**Option B : 45 + 3.50(x – 1) ≤ 200**

**SAT Math Question No 9:**

Hamadi is renting a car. With his extreme coupons, the rental charge is $17.50 per day plus $0.16 per mile. His company will reimburse Hamadi for $33 of this portion of the travel expenses. If he rents the car for one day, what is one possible number of miles paid for by the company?

**Option A** : 53

**Option B** : 97

**Option C** : 110

**Option D** : 150

**Show/Hide Answer Key**

**Option A : 53**

**SAT Math Question No 10:**

To get to school, Da’Quon walks 0.6 miles from his house to the bus stop. He then takes the bus for 3.9 miles. After he gets off the bus, he can choose one of several walking routes to school. The total amount of miles he travels, via walking and bus, does not exceed 5.4. What is the greatest possible number of miles he walks after getting off the bus?

**Option A** : 0.0 miles

**Option B** : 0.3 miles

**Option C** : 0.9 miles

**Option D** : 1.5 miles

**Show/Hide Answer Key**

**Option C: 0.9 miles**

**SAT Math Question No 11:**

Karim has a $35 gift card to his favorite restaurant. Meal tax in his area is 14.3%. Karim would also like to leave a $5 tip. If c represents Karim’s pre-tax bill, and he wants to pay the entire meal amount, including tip and tax, using the gift card, which of the following inequalities best models the situation described above?

**Option A** : 1.143c – 5 ≥ 35

**Option B** : 1.143c + 5 ≤ 35

**Option C** : 0.143c – 5 ≤ 35

**Option D** : 0.143c + 5 ≥ 35

**Show/Hide Answer Key**

**Option B : 1.143c + 5 ≤ 35**

**SAT Math Question No 12:**

One of the rules in a public speaking contest requires contestants to speak for as close to 3 minutes (180 seconds) as possible. Contestants lose 2 points for each second they speak either over or under the 3 minutes. If a contestant lost 18 points, what are the possible lengths of time they spoke?

**Option A** : 171 and 186 seconds

**Option B** : 174 and 186 seconds

**Option C** : 171 and 189 seconds

**Option D** : 174 and 189 seconds

**Show/Hide Answer Key**

**Option C : 171 and 189 seconds**

**SAT Math Question No 13:**

A company’s unit cost for producing x units is a minimum when x=2,000 units are produced. The unit cost increases $0.25 for every unit more or less than 2,000 produced. Which of the following could be the number of units for which the unit cost increases by $7.50 from the minimum?

**Option A** : 1700 or 2300

**Option B** : 1975 or 2025

**Option C** : 1997 or 2003

**Option D** : 1970 or 2030

**Show/Hide Answer Key**

**Option D : 1970 or 2030**

**SAT Math Question No 14:**

Aria is buying refreshments for a birthday party. She intends to get an ice cream cake for $23 and some cupcakes for $2 each. Aria has a $45 budget but does not have to spend the entire amount. Which inequality best represents the number of cupcakes, c, that Aria can purchase?

**Option A** : c > 11

**Option B** : c < 11

**Option C** : c ≥ 11

**Option D** : c ≤ 11

**Show/Hide Answer Key**

**Option D : c ≤ 11 **

**SAT Math Question No 15:**

Stan is crocheting scarves to sell at a craft fair. He will give away the first 2 scarves that he crochets and will sell the rest at the craft fair for $8 each. His scarves are very popular and people always buy all that he is willing to sell. Stan’s goal is to earn at least $75 at the craft fair. If n represents the number of scarves which Stan needs to crochet to meet his goal, which of the following inequalities best models the situation described above?

**Option A** : 8n – 2 ≥ 75

**Option B** : 8n ≥ 75 – 2

**Option C** : 8(n – 2) ≥ 75

**Option D** : (8 – 2)n ≥ 75

**Show/Hide Answer Key**

**Option C : 8(n – 2) ≥ 75**

### SAT 2022 Math Grid-in Practice Questions

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

**SAT Math Question No 16:**

One particular hotel in the downtown area costs $90 a night. An additional 10% tax is added to the original cost of the hotel room. There is also a one-time $12 parking charge, and a family can expect to spend $30 on tips during their stay. How many nights can a family spend at the hotel without exceeding their budget of $600?

**Show/Hide Answer Key**

**Correct Answer : 5**

**SAT Math Question No 17:**

Christopher has at most $18.50 to spend at a convenience store. He buys one bag of bananas for $1.50 and a bottle of apple juice for $1.55. If gasoline at this store costs $2.35 per gallon, which of the following number of gallons can he buy for his car without exceeding his budget?

**Show/Hide Answer Key**

**Correct Answer : 4.23**

**SAT Math Question No 18:**

Trevon is going to buy a coat and a hat. The coat costs 3 times as much as the hat. He must spend less than $94. If the cost of the hat costs x dollars, which inequality best models this situation?

**Show/Hide Answer Key**

**Correct Answer : 4x < 94**

**SAT Math Question No 19:**

Yong needs to cut a 3 foot long board into several 2 inch lengths. With each cut, his saw blade shaves off an additional 1/8 inch of the board. What is the maximum number of full 2 inch lengths that Yong can cut from his board?

**Show/Hide Answer Key**

**Correct Answer : 17**

**SAT Math Practice Test Question No 20:**

Ella needs a 70% isopropyl alcohol solution as an antiseptic. She has a 100 milliliter (ml) container of 90% isopropyl alcohol solution. Approximately how much water should Ella add to dilute it to a 70% isopropyl alcohol solution? Round to the nearest tenth.

**Show/Hide Answer Key**

**Correct Answer : 28.6 ml of water**