Age word problems
Ex 1 Age word problem Imran is 18. Diya is 2. How many years will it take for Imran to be 3 times as old as Diya?
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- 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!
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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