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

- [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.