Main content

## Algebra 1

### Unit 7: Lesson 3

Modeling with linear inequalities- Writing two-variable inequalities word problem
- Solving two-variable inequalities word problem
- Interpreting two-variable inequalities word problem
- Two-variable inequalities word problems
- Modeling with systems of inequalities
- Writing systems of inequalities word problem
- Solving systems of inequalities word problem
- Graphs of systems of inequalities word problem
- Systems of inequalities word problems
- Graphs of two-variable inequalities word problem
- Inequalities (systems & graphs): FAQ
- Creativity break: What can we do to expand our creative skills?

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Solving systems of inequalities word problem

CCSS.Math:

Given a system of linear inequalities that models a context about making chairs and tables, Sal finds how many can be made.

## Want to join the conversation?

- Can two-variable linear inequalities (if you have two of them) be solved like systems of equations, with substitution and elimination, instead of just using the graphing method?(7 votes)
- I do not think so, when doing systems of equations we are just solving for the coordinates where both of the lines crosses. In systems of inequalities we solve for the area that results for overlaping the two inequalities. I might be wrong, so iam waiting for the answer aswell.(6 votes)

- How do you write a real world word problem for inequalities(3 votes)
- Say you have
**s**grams of sugar and**f**grams of flower and you can make 1 batch of cookies for**x**and one batch of cupcakes for**y**how many of each can you make if you want to use up as much as you can?(1 vote)

- how do you demonstrate that both x and y can not be negative numbers in any given problem using inequalities?(1 vote)
- When a third of unknown number is added to two, the result is not greater than the number subtracted from one. Find the range of values of the number(1 vote)
- Amended via comment

1/3 x + 2 ≤ 1 - x, add x and -2 to get 4/3x ≤ -1, multiply by reciprocal to get x ≤ - 3/4.(1 vote)

- I found the zeroes and got a different answer. I got that she was short on boards, not nails. Maximum 8 tables for 150 nails. Am I right?(1 vote)
- I think you got your answer by substituting C=0 into the first inequality. So, you found 1 point for the 1st inequality. It tells you nothing about the solution to the system of equations.

The problem gives you a specific ordered pair and asks you to determine if it satisfies both inequalities. It doesn't. Sal's work is the correct approach given the requirements stated for this problem.

Hope this helps.(0 votes)

## Video transcript

- [Voiceover] "Fleur wants
to make tables and chairs. "Each chair or table is
made with the same number "of wooden boards and nails. "She has a total of 150 wooden boards and 330 nails. "The following inequality
represents the number "of tables, T, and chairs, C, "she can make with 150 wooden boards." So we can see the 150 wooden
boards right over here and it looks like she uses 17
wooden boards for each table so the total amount of
boards from the tables are to make the tables is 17 T. And it looks like she
uses six wooden boards for each chair and that's why you take six per chair times the number of chairs. This is the total number of wooden boards she uses from the chairs. And you add them together. It can't be anymore than 150. She only has, I guess 150 wooden boards. "Additionally, the following
inequality represents "the number of tables and chairs "she can make with 330 nails." So once again, she has
the maximum of 330 nails. It looks like she needs 34 nails per table because the total nails from the tables is 34 nails per table times
the number of tables. And then it looks like she needs 27 nails. It looks like she needs 27 nails per chair because the total nails that she uses in all of the chairs
are 27 nails per chair times the number of chairs. "Does Fleur have enough boards "and nails to make three tables, "to make three, "to make three tables and nine chairs? "And nine chairs?" Let's see, let's look
at the number of boards. To make three tables and nine chairs, she's going to use 17 times T. In this case, it's three. Shes' going to use 17 times
three boards for the tables and then she is going to use, she is going to use six times the number of chairs. So six times nine chairs. Six boards per chair times nine chairs. So six times nine is the number of boards she's going to use on the chairs. So this is going to,
this is the same thing as 17 times three is 51. 51 plus, six times nine is 54. So this is 54. And what is this? Is this less than or equal to 150? Is that less than or equal to 150? Let's see, 51 plus 54 is going to be 105. So that indeed is less
than or equal to 150. So that checks out. So she has more than enough boards. So she has enough boards. Let me write that. Enough boards. Now let's see if she has enough nails. Let's see if she has, that came out weird, enough boards. Let's see if she has enough nails. So three tables are going to require 34 times three nails. So 34 nails per table times three tables. So 34 times three. That's how many nails
for all of the tables. And then plus, if she is going to use 27 nails per chair times the nine chairs. 27 times nine. We need to figure out, is this less than or equal to 330? And so let's see. 34 times three, that is 100. No, that's 90 plus 12. So that's 102 and then 27 times nine. So let's see, that would be, was it 243? Yep, so plus 243. So it's 102 plus 243, is that less than or equal to 330? So let's see, this would be, this would end up adding up to 345. No, this is not less than or equal to 330. This is not the case. This is not true. Not true. So she does not have enough nails. So not enough, not enough nails. And so she has enough
boards but not enough nails. So unless she goes and buys some nails, she's not going to be able to
make these tables and chairs.