Analyzing structure with linear inequalities: fruits

Shantanu bought more apples than bananas and he bought more bananas and cantaloupes let a represent the number of apples Shantanu bought let B represent the number of bananas and let's see 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 alright 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 and 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't rise let's use let's let's 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 and would say hey there's not enough information to tell and general this is a good strategy for things like this where we were 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 let's see if we can make B plus C greater than a so the most have to be less than a so let's see if C is C is 5 and B is 6 and let's make a 7 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 6 5 we can make a bigger than 6 plus 5 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 that there is not enough information to tell now one thing that we yeah there's 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 eleven then B plus C is equal to a so basically the information they gave us any of these are actually possible so there's not enough information to tell