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A cargo helicopter delivers only 100-pound packages and 120-pound packages. For each delivery trip, the helicopter must carry at least 10 packages, and the total weight of the packages can be at most 1,100 pounds. What is the maximum number of 120-pound packages that the helicopter can carry per trip?

The point $(8,2)$ in the xy-plane is a solution to which of the following systems of inequalities?

Adam’s school is a 20-minute walk or a 5-minute bus ride away from his house. The bus runs once every 30 minutes, and the number of minutes, w, that Adam waits for the bus varies between 0 and 30. Which of the following inequalities gives the values of w for which it would be faster for Adam to walk to school?

Marisa needs to hire at least 10 staff members for an upcoming project. The staff members will be made up of junior directors, who will be paid $640 per week, and senior directors, who will be paid $880 per week. Her budget for paying the staff members is no more than $9,700 per week. She must hire at least 3 junior directors and at least 1 senior director. Which of the following systems of inequalities represents the conditions described if x is the number of junior directors and y is the number of senior directors?

Valentina bought two containers of beads. In the first container 30% of the beads are red, and in the second container 70% of the beads are red. Together, the containers have at least 400 red beads. Which inequality shows this relationship, where x is the total number of beads in the first container and y is the total number of beads in the second container?

The total cost, in dollars, to rent a surfboard consists of a $\$25$ service fee and a $\$10$ per hour rental fee. A person rents a surfboard for $t$ hours and intends to spend a maximum of $\$75$ to rent the surfboard. Which inequality represents this situation?

In North America, the standard width of a parking space is at least 7.5 feet and no more than 9.0 feet. A restaurant owner recently resurfaced the restaurant’s parking lot and wants to determine the number of parking spaces, n, in the parking lot that could be placed perpendicular to a curb that is 135 feet long, based on the standard width of a parking space. Which of the following describes all the possible values of n ?

A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35  pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are nonnegative integers. Which of the following systems of inequalities best represents this situation?

Which of the following ordered pairs is a solution to the system of inequalities above?

On a car trip, Rhett and Jessica each drove for part of the trip, and the total distance they drove was under $220$ miles. Rhett drove at an average speed of $35 \text{miles} \text{per} \text{hour} \left(\text{mph}\right)$, and Jessica drove at an average speed of $40 \text{mph}$. Which of the following inequalities represents this situation, where $r$ is the number of hours Rhett drove and $j$ is the number of hours Jessica drove?

A local transit company sells a monthly pass for $95 that allows an unlimited number of trips of any length. Tickets for individual trips cost $1.50, $2.50, or $3.50, depending on the length of the trip. What is the minimum number of trips per month for which a monthly pass could cost less than purchasing individual tickets for trips?

A bakery sells trays of cookies. Each tray contains at least 50 cookies but no more than 60. Which of the following could be the total number of cookies on 4 trays of cookies?

$y\le x+7$

$y\ge -2x-1$

Which point $\left(x,y\right)$ is a solution to the given system of inequalities in the xy-plane?

A salesperson’s total earnings consist of a base salary of $x$ dollars per year, plus commission earnings of $11\%$ of the total sales the salesperson makes during the year. This year, the salesperson has a goal for the total earnings to be at least $3$ times and at most $4$ times the base salary. Which of the following inequalities represents all possible values of total sales $s$, in dollars, the salesperson can make this year in order to meet that goal? 

Ty set a goal to walk at least $24$ kilometers every day to prepare for a multiday hike. On a certain day, Ty plans to walk at an average speed of $4$ kilometers per hour. What is the minimum number of hours Ty must walk on that day to fulfill the daily goal?

A number $x$ is at most $2$ less than $3$ times the value of $y$. If the value of $y$ is $-4$, what is the greatest possible value of $x$?

Tom scored 85, 78, and 98 on his first three exams in history class. Solving which inequality gives the score, G, on Tom’s fourth exam that will result in a mean score on all four exams of at least 90 ?

$y<-4x+4$

Which point ($x$, $y$) is a solution to the given inequality in the $xy$-plane?

A certain elephant weighs 200 pounds at birth and gains more than 2 but less than 3 pounds per day during its first year. Which of the following inequalities represents all possible weights w, in pounds, for the elephant 365 days after birth?

The Karvonen formula above shows the relationship between Alice’s target heart rate H, in beats per minute (bpm), and the intensity level p of different activities. When , Alice has a resting heart rate. When , Alice has her maximum heart rate. It is recommended that p be between 0.5 and 0.85 for Alice when she trains. Which of the following inequalities describes Alice’s target training heart rate?

A small business owner budgets $\$\mathrm{2,200}$ to purchase candles. The owner must purchase a minimum of $200$ candles to maintain the discounted pricing. If the owner pays $\$4.90$ per candle to purchase small candles and $\$11.60$ per candle to purchase large candles, what is the maximum number of large candles the owner can purchase to stay within the budget and maintain the discounted pricing?

A number $x$ is at most $17$ less than $5$ times the value of $y$. If the value of $y$ is $3$, what is the greatest possible value of $x$?

A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, p people chose the first picture in the set. If more than 20% of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of p ?

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. If a triangle has side lengths of $6$ and $12$, which inequality represents the possible lengths, $x$, of the third side of the triangle?

The shaded region shown represents solutions to an inequality. Which ordered pair $\left(x,y\right)$ is a solution to this inequality?