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Sal solves the following age word problem: Arman is 18. Diya is 2. How many years will it take for Arman to be 3 times as old as Diya? Created by Sal Khan.
Video transcript
Let's say that Arman today is 18 years old And let's say that Diya today, is 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 How many years, will it take for Arman to be 3 times as old as Diya? So 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 it will 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 some variable, let's say y will be years Let's say y is equal to 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 old Arman will be in y years Well in y years, Arman is going to be how old? Arman is going to be, well he's 18 right now And in y years, he is going to be y years older So, 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 years she'll just be 2 plus y So what we're curious about now that we know this Is how many years will it take for this quantity, for this expression, to be 3 times this quantity So we're really curious We wanna solve for y, such that 18 plus y is going to be equal to 3 times, 2 plus y Notice, this is Arman in y years, this is Diya in y years And we were saying that what Arman is going to be in y years is 3 times what Diya 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, maybe I'll do this in a new colour just so I don't have to keep switching So on the left hand side, I still have 18 plus y And on the right hand side, I can just 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 we have our "3y" over here we have more "y"s here on the right hand side than on the left hand side So let's get rid of the y's on the left hand side You can do it either way but you'd end up with negative numbers So let's subtract a y, from each side And we are left with On the left hand side, 18 And on the right hand side, you have 6 Plus 3 y's take away one of those y's You're gonna be left with 2 y's Now, we can get rid of the constant term here So, we will 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 0, so you have 12 is equal to 2y 2 times the number of years it will take Is 12, and you can probably solve this in your head But if we just want a one coefficient here we divide by 2 on the right Whatever we do to one side of the equation we have to do it on the other side Otherwise the equation will not still be an equation So we are left with, y is equal to 6 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 6 years Now, I want you to verify this Think about it, is this actually true? Well, in 6 years how old is Arman going to be? He's going to be 18 plus 6, we now know that this thing is 6 In 6 years, Arman is going to be 18 plus 6 which is 24 years old How old is Diya 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 6 years, Arman is 24 and Diya is 8, Arman is 3 times as old as Diya And we are done!