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# Age word problem: Arman & Diya

CCSS.Math:

## Video transcript

let's say that arm on today is 18 years old 18 years old and let's say that dia dia today is 2 2 years old and what I am curious about in this video is how many years will it take and let me write this down Oh many years will it take will it take for Arman or Arman to be 3 times times as old as Thea as DSO that's the question right there and I encourage you to try to take a shot at this yourself so let's think about this a little bit we're asking how many years will it take that's what we don't know that's what we're curious about how many years will it take for Arman to be 3 times as old as diya so let's set let's set some variable let's say Y 4 years let's say Y is equal to years years it will take so given that can we now set up an equation given this information to figure out how many years it will take for Arman to be 3 times as old as diya well let's think about how how old Arman will be in Y years how old will he be well in Y years let me write it here in in Y years Arman Arman Arman is going to be how old Arman is going to be well he's 18 right now and in Y years he's going to be Y years older so in in Y years Arman is going to be 18 plus y and what about diya how old will she be how old will she be in Y years well she's 2 now and in Y here she'll just be 2 plus y so what we're curious about now that we know this is how many years it will take for this quantity for this expression to be three times this quantity so we're really curious we want to solve for y such that 18 plus y is going to be equal to three x is going to be equal to 3 times 2 plus y 3 times 2 plus y notice this is our mod and Y years this is dia and Y years and we're saying that what our mod is going to be in Y years is three times what Thea is going to be in Y years so we've set up our equation now we can just solve it so let's take this step by step so on the left hand side and maybe I'll do this in a new color just so I don't have to keep switching so the left hand side I still have 18 plus y and on the right hand side I can distribute this 3 so 3 times 2 is 6 3 times y is 3y 6 plus 3y and then it's always nice to get all of our constants on one side of the equation all of our variables on the other side of the equation so let's we have a 3y over here we have more Y's on the right hand side than the left hand side so let's get rid of the Y's on the left hand side you could do it either way but you would end up with negative numbers so let's subtract 2y from each side and we are left with we are left with on the left hand side 18 and on the right hand side you have 6 plus 3 wise take away one of those Y's you're going to be left with 2 wise now we can get rid of the constant term here so we will subtract 6 from both sides subtract 6 from both sides 18 minus 6 is 12 the whole reason why we subtracted 6 from the right was to get rid of this 6 minus 6 is zero so you have 12 is equal to 2y 2 times the number of years it will take is 12 and you could probably solve this in your head but if we just want a 1 coefficient here we would divide by 2 on the right whatever we do to one side of equation we have to do it on the other side otherwise the equation will not still be an equation so we are left with we are left with Y is equal to S X or Y is equal to 6 so going back to the question how many years will it take for Arman to be 3 times as old as diya well it's going to take six years now I want you to verify this think about it is this actually true well in 6 years how old Arman going to be he's going to be 18 plus 6 we now know that this thing is 6 so in in six years in six years Arman is going to be 18 plus 6 which is 24 years old how old is there going to be well she's going to be 2 plus 6 which is 2 plus 6 which is 8 years old and lo and behold 24 is indeed 3 times as old as 8 in in 6 years our mom's 24 D is 8 Arman is 3 times as old as the ax and we are done