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Solving systems of inequalities word problem

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

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  • duskpin ultimate style avatar for user Zingo
    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)
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  • blobby green style avatar for user Becky Harris
    How do you write a real world word problem for inequalities
    (3 votes)
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  • male robot johnny style avatar for user yahyayanes1
    how do you demonstrate that both x and y can not be negative numbers in any given problem using inequalities?
    (1 vote)
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  • blobby green style avatar for user comfortbansah30
    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)
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  • primosaur seedling style avatar for user Crystal
    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)
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    • stelly blue style avatar for user Kim Seidel
      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.