- Solving linear equations and linear inequalities | Lesson
- Understanding linear relationships | Lesson
- Linear inequality word problems | Lesson
- Graphing linear equations | Lesson
- Systems of linear inequalities word problems | Lesson
- Solving systems of linear equations | Lesson
- Systems of linear equations word problems | Lesson
Systems of linear inequalities word problems | Lesson
What are systems of linear inequalities word problems, and how frequently do they appear on the test?
Note: On your official SAT, you'll likely see at most 1 question that tests your ability to write and solve systems of linear inequalities based on real-world scenarios. Make sure you understand the more frequently-tested skills on the SAT before you spend time practicing this skill.
A system of linear inequalities is just like a system of linear equations, except it is composed of inequalities instead of equations.
Systems of linear inequalities are used to model scenarios with multiple constraints.
For example: You're buying snacks for a party; you want to buy enough so that you don't run out (snacks what people will eat), but you also don't want to overspend (money spent on snacks budget for the party). If you manage to buy enough snacks without breaking your budget, you've solved a system of inequalities!
This lesson builds upon an understanding of the following skills:
You can learn anything. Let's do this!
How do I write systems of linear inequalities based on word problems?
Translating systems of inequalities word problems
Systems of linear inequalities word problems
On the SAT, systems of linear inequalities word problems are some of the longest questions you'll read. This can be intimidating, but don't worry—their bark is worse than their bite!
On the test, we may be asked to:
- Write our own system of linear inequalities based on the word problem (frequent)
- Find a solution to the system we wrote (infrequent)
What are some key phrases to look out for?
Systems of linear inequality word problems share the same common key phrases as linear inequality word problems, as shown in the table below.
Note: is a constant in the examples.
|"More than ", "greater than ", or "higher than "|
|"Less than " or "lower than "|
|"Greater than or equal to " or "at least "|
|"Less than or equal to " or "at most "|
|"No less than "|
|"No more than "|
|"Least", "lowest", or "minimum" value||The smallest value that satisfies the inequality|
|"Greatest", "highest", or "maximum" value||The largest value that satisfies the inequality|
|"A possible" value||Any value that satisfies the inequality|
Let's look at some examples!
Diego works at a scooter dealership that sells two scooter models: a standard model and a racing model. Last month, his goal was to sell at least scooters. If Diego met his goal and brought in over in sales, which of the following systems of inequalities describes , the possible number of standard model scooters, and , the possible number of racing model scooters, that Diego sold last month?
Eugenia wants to buy at least prizes for rewarding her students throughout the semester. The prize pool will be made of small and large prizes, which cost and each respectively. Her budget for the prizes can be no more than . She wants to buy at least small prizes and at least large prizes. Which of the following systems of inequalities represents the conditions described if is the number of small prizes and is the number of large prizes?
If Eugenia buys large prizes, what is a possible number of small prizes she can buy to satisfy the conditions described?
Try: write a system of linear inequalities
A warehouse worker uses a forklift to move boxes that weigh either pounds or pounds each. Let be the number of -pound boxes and be the number of -pound boxes. The forklift can carry up to either boxes or a weight of pounds.
The total number of boxes the forklift can carry is
The total weight the forklift can carry is
Write an inequality that models the number of boxes the forklift can carry. The inequality should contain , , and an inequality sign.
Write an inequality that models the amount of weight the forklift can carry. The inequality should contain , , and an inequality sign.
Practice: write a system of linear inequalities
Diamond has two jobs. She works as a barista, which pays per hour, and she works as an illustrator, which pays per hour. She wants to work no more than hours and to earn at least per week. Her barista job schedules her for up to hours per week. Which of the following systems of inequalities represents this situation in terms of and , where is the number hours Diamond works as a barista and is the number of hours she works as an illustrator?
Practice: solve a system of linear inequalities
A cargo van delivers only -pound and -pound packages. For each delivery trip, the van must carry at least packages, and the total weight of the packages cannot exceed pounds. What is the maximum number of -pound packages that the van can carry per trip?
Want to join the conversation?
- In the practice questions, word problems of inequalities with graphs are also included? Where can I find a lesson to understand those?(12 votes)
- Hey, in the Deigo question, can the variables be (1,35) as well ?(2 votes)
- All real numbers can be the solution for the racing model variable(3 votes)
- is studying all sat resources enough to score 1400 in 1,5 months ?(1 vote)
- What you’ll need to score a 1400 or above will depend on your pre-existing skills, your learning style, how much you practice, etc. I will say that there are definitely people who only practice on Khan and do score that high.
I'd suggest taking one practice SAT just to get a baseline, first.(4 votes)
- What is difference between SAT and LCAT (LUMS Common Admission Test)? I mean,to what extent do they differ?(0 votes)