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Current time:0:00Total duration:2:49

Systems of linear inequalities word problems — Harder example

Video transcript

- [Male Voice Narrator] A cell phone producer distributes boxes of units to retail stores. A unit is either a cell phone or an accessory, and each box can have up to 24 units composed of c cellphones and a accessories. In addition, each box must have at least as many cell phones as accessories. At least as many cell phones as accessories. Which of the following systems of inequalities best models the situation described above? So, let's just think it through. So each box can have up to 24 units composed of c cellphones and a accessories. So that means that the c cellphones plus the a accessories, it can be up to 24 units. So it has to be less than or equal to 24. This is the number of cellphones, this is the number of accessories, you add them together, it has to be up to 24. And then they tell us, and then they tell us, right over here, each box must have at least as many cellphones as accessories. So the cellphones have to be greater than or equal to the accessories. Alright. Those are the constraints. So let's see which of these choices match them. So, this one says 24 is less than or equal to a plus c. No, it should be the other way round. It should be 24 should be greater than or equal to a plus c. This is saying that a plus c needs to be 24 or above, but they say each box can have up to 24 cell units. They can't have 25 units or anything like this. So this is saying the opposite thing than what this is saying. This is saying c plus a has to be less than or equal to 24. This is saying 24 has to be less than or equal to c plus a or a + c, so we can just rule that one out. This one also has that same 24 is less than or equal to a plus c, so we can just rule that one out. This one over here. Let's see, a plus c is less than or equal to 24, well, that's exactly what we have right over here, they just swapped the a and the c; a plus c is less than or equal to 24. And then over here they have a is less than or equal to c, which is equivalent to what this is, saying c is greater than or equal to a. This is the same thing as saying that a is less than or equal to c. So this is the choice I'd go with. This choice right over here has this constraint right, but then it says that the number of cellphones has to be no more than the number of accessories. Another way to think about it is at least as many accessories as cellphones which is the opposite, is not what this constraint is saying. So we could rule that out as well.