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## Modeling with linear inequalities

Current time:0:00Total duration:3:53

# Analyzing structure with linear inequalities: fruits

## Video transcript

- [Instructor] Shantanu bought
more apples than bananas and he bought more
bananas than cantaloupes. Let A represent the number
of apples Shantanu bought, let B represent the number of bananas, and let C represent the
number of cantaloupes. Let's compare the
expressions B plus C and A. Which statement is correct? So is B plus C greater than A? Is it less than A? Or are these two quantities equal? Or is there not enough
information to tell? So like always, pause this video and see if you can work
through it on your own and now I will work through it with you. All right, so let's just
write down the information that they gave us. They say let A represent the number, well that's more straightforward, A for apple, B for
banana, C for cantaloupe. Here we have more apples than bananas, so A is greater than B, and then they also tell
us he bought more bananas than cantaloupes, so B is greater than C, or we could rewrite that as A is greater than B is greater than C or we could write that as C
is less than B is less than A. This is essentially the
information that they give us. So let's see, which of
these is going to be true? B plus C greater than A, B plus C greater than A, B plus C less than A. So one thing that we can
try is let's try to plug in some values, some numbers to see if we can get combinations that are consistently
in one of these buckets or if they fall into
multiple of these choices, then we say hey there's not
enough information to tell. In general, this is a good
strategy for things like this where we're dealing with
very abstract quantities. So let's make a little table here. So A, B, C and then I can also figure
out what B plus C is. So this is going to be A, B, C, and this is B plus C and
we can compare that to A. So let's see a situation where let's see if we can make
B plus C greater than A. So they both have to be less than A. So let's see, if C is five and B is six and let's make A seven. So in this situation, B plus
C is going to be equal to 11. So we're able to find a situation where if B plus C are close enough to A, that B plus C is going
to be greater than A. So we're able to find this scenario. Let's see if we can figure out a scenario where B plus C is less than A. Well if, well we could do the
same B plus C, six, five. We could make A bigger than six plus five. We can make A 12. And now this is a situation, so this first situation we have
B plus C is greater than A. The second situation right over here, you have B plus C is less than A and so depending on what
your A, B, and C's are that meet these constraints and notice, both of these situations
I meet all the constraints where A is greater than
B is greater than C, but it could be either one of these. So that immediately tells us that there is not enough
information to tell. Now, one thing that we, yeah there's just not
enough information to tell. I can even come up with a scenario where B plus C is equal to A. If it's six, five, and 11. Then B plus C is equal to A. So based on the information they gave us, any of these are actually possible. So there's not enough information to tell.