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Current time:0:00Total duration:3:43

Topic D: Systems of linear equations and their solutions

Video transcript

we're told that in 40 years Emraan will be 11 times as old as he is right now and then we're asked how old is he right now and so I encouraged you to try this on your own well let's see if we can set this up as an as an equation so let's let's figure out what our unknown is first well our unknown is how old he is right now so let's let let's let and I'm just arbitrarily using X we always like to use X what I could have you really set it to be anything but let's say X is equal to how old he is right now how old not how old how old he is now now what do we know about how old he will be in 40 years well he's going to be how old he is now plus 40 so let me write that down so in in 40 years in 40 years Imran is going to be x plus 40 plus plus 40 plus this 40 right over here but they give us another piece of information this by itself isn't enough to figure out how old he is right now but they tell us in 40 years so in 40 years Imran will be Imran will be 11 times as old as he is right now so that's saying that this quantity right over here X plus 40 is going to be 11 times X in 40 years he's going to be 11 times as old as he is right now so this is going to be times 11 you take X multiply it times 11 you're going to get how old he's going to be in 40 years so let's write that down as an equation you take X you take X multiply it by 11 so 11 times as old as he is right now is how old he is going to be in 40 years is how old he is going to be in 40 years and we have set up a nice little tidy linear equation now so we just have to solve for X so let's get all the X's on the left-hand side we have more X's here than on the right-hand side so so we avoid negative numbers let's take all the x's here so if I want to get rid of this X on the right-hand side I want to subtract an X but obviously I can't just do it to the right otherwise equality won't be true anymore I need to do it on the left as well and so I am left with 11 if I have 11 or something and I take away one of them I'm left with 10 of that something so I'm left with 10 times X 10 times X is equal to well these X is X minus X just zero that was the whole point it's going to be equal to 40 and you could do this in your head at this point but let's just solve it formally so if we want a 1 coefficient here we'd want to divide by 10 but we've got to do that to both sides and so we are left with and we can have our drumroll now we are left with X is equal to 4 years old X is equal to 4 so our answer the question how old is Imraan right now he is 4 4 years old and let's verify this if he's 4 years old right now in 40 years he's going to be 44 years old and 44 years old is indeed 11 times older than 4 years old you definitely this is a factor of 11 here so it all worked out