In the practice questions, word problems of inequalities with graphs are also included? Where can I find a lesson to understand those?

Is this what you are looking for? https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:inequalities-systems-graphs/x2f8bb11595b61c86:modeling-with-linear-inequalities/v/graph-of-system-of-inequalities-word-problem

Hey, in the Deigo question, can the variables be (1,35) as well ?

All real numbers can be the solution for the racing model variable

is studying all sat resources enough to score 1400 in 1,5 months ?

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.

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SAT

Course: SAT > Unit 6

Lesson 3: Heart of Algebra: lessons by skill

Systems of linear inequalities word problems | Lesson

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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 is greater than or equal to what people will eat), but you also don't want to overspend (money spent on snacks is less than or equal to 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

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Writing systems of inequalities word problemSee video transcript

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: c is a constant in the examples.

Phrase	Translates to...
"More than c", "greater than c", or "higher than c"	is greater than, c
"Less than c" or "lower than c"	is less than, c
"Greater than or equal to c" or "at least c"	is greater than or equal to, c
"Less than or equal to c" or "at most c"	is less than or equal to, c
"No less than c"	is greater than or equal to, c
"No more than c"	is less than or equal to, c
"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 dollar sign, 5, comma, 000 standard model and a dollar sign, 7, comma, 000 racing model. Last month, his goal was to sell at least 36 scooters. If Diego met his goal and brought in over dollar sign, 250, comma, 000 in sales, which of the following systems of inequalities describes s, the possible number of standard model scooters, and r, the possible number of racing model scooters, that Diego sold last month?

[Show me the translation!]

[Show me a possible solution!]

Eugenia wants to buy at least 30 prizes for rewarding her students throughout the semester. The prize pool will be made of small and large prizes, which cost dollar sign, 2 and dollar sign, 5 each respectively. Her budget for the prizes can be no more than dollar sign, 100. She wants to buy at least 15 small prizes and at least 5 large prizes. Which of the following systems of inequalities represents the conditions described if x is the number of small prizes and y is the number of large prizes?

[Show me the translation!]

If Eugenia buys 10 large prizes, what is a possible number of small prizes she can buy to satisfy the conditions described?

[Show me a possible solution!]

Try it!

Try: write a system of linear inequalities

A warehouse worker uses a forklift to move boxes that weigh either 45 pounds or 70 pounds each. Let x be the number of 45-pound boxes and y be the number of 70-pound boxes. The forklift can carry up to either 60 boxes or a weight of 3000 pounds.

The total number of boxes the forklift can carry is

60.

The total weight the forklift can carry is

3000 pounds.

Write an inequality that models the number of boxes the forklift can carry. The inequality should contain x, y, and an inequality sign.

Write an inequality that models the amount of weight the forklift can carry. The inequality should contain x, y, and an inequality sign.

Your turn!

Practice: write a system of linear inequalities

Diamond has two jobs. She works as a barista, which pays dollar sign, 13 per hour, and she works as an illustrator, which pays dollar sign, 30 per hour. She wants to work no more than 45 hours and to earn at least dollar sign, 625 per week. Her barista job schedules her for up to 30 hours per week. Which of the following systems of inequalities represents this situation in terms of x and y, where x is the number hours Diamond works as a barista and y is the number of hours she works as an illustrator?

(Choice A)
$\begin{aligned} &x+y\geq 45 \\\\ &13x+30y \geq 625 \\\\ &x \geq30 \end{aligned}$
(Choice B)
$\begin{aligned} &x+y\geq 45 \\\\ &13x+30y \leq 625 \\\\ &x \leq 30 \end{aligned}$
(Choice C)
$\begin{aligned} &x+y\leq 45 \\\\ &13x+30y \geq 625 \\\\ &x \leq 30 \end{aligned}$
(Choice D)
$\begin{aligned} &x+y\leq 45 \\\\ &13x+30y \leq 625 \\\\ &x \leq 30 \end{aligned}$

Practice: solve a system of linear inequalities

A cargo van delivers only 50-pound and 80-pound packages. For each delivery trip, the van must carry at least 20 packages, and the total weight of the packages cannot exceed 1, comma, 500 pounds. What is the maximum number of 80-pound packages that the van can carry per trip?

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ritikasinghal5537
Posted 2 years ago. Direct link to ritikasinghal5537's post “In the practice questions...”
In the practice questions, word problems of inequalities with graphs are also included? Where can I find a lesson to understand those?
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- 22yangj
  Posted 2 years ago. Direct link to 22yangj's post “Is this what you are look...”
  Is this what you are looking for?
  https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:inequalities-systems-graphs/x2f8bb11595b61c86:modeling-with-linear-inequalities/v/graph-of-system-of-inequalities-word-problem
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Ananya Pandey
Posted a year ago. Direct link to Ananya Pandey's post “Hey, in the Deigo questio...”
Hey, in the Deigo question, can the variables be (1,35) as well ?
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(2 votes)
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- fardeenfahim
  Posted a year ago. Direct link to fardeenfahim's post “All real numbers can be t...”
  All real numbers can be the solution for the racing model variable
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hpro048
Posted 9 months ago. Direct link to hpro048's post “is studying all sat resou...”
is studying all sat resources enough to score 1400 in 1,5 months ?
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- Johanna
  Posted 9 months ago. Direct link to Johanna's post “What you’ll need to score...”
  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.
  Button navigates to signup page
  (4 votes)
Imran Uddin
Posted 5 months ago. Direct link to Imran Uddin's post “What is difference betwee...”
What is difference between SAT and LCAT (LUMS Common Admission Test)? I mean,to what extent do they differ?
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