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### Course: Algebra 1 > Unit 6

Lesson 6: Systems of equations word problems- Age word problem: Imran
- Age word problem: Ben & William
- Age word problem: Arman & Diya
- Age word problems
- System of equations word problem: walk & ride
- Systems of equations word problems
- System of equations word problem: no solution
- System of equations word problem: infinite solutions
- Systems of equations word problems (with zero and infinite solutions)
- Systems of equations with elimination: TV & DVD
- Systems of equations with elimination: apples and oranges
- Systems of equations with substitution: coins
- Systems of equations with elimination: coffee and croissants
- Systems of equations: FAQ

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# Age word problem: Arman & Diya

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.

## Want to join the conversation?

- I understand the video, but I have trouble answering the problems on my own. I don't understand which one you are supposed to times and how you are supposed to tell. For example: Daniel is 40 years older than Vanessa. 12 years ago, Daniel was 3 times older than Vanessa.

Which part of the equation do you times? I thought it was Vanessa's part (the smaller one) to make it the same amount as Daniel's but I keep making errors and am not getting anywhere.

I know the example I have made does not make any sense, but if you could just show the process and how to put each part into the equation, I'd be grateful as I'm getting very frustrated!(54 votes)- Don't worry! There's always something you don't know!

It takes patience and courage! One day you will master it!

@Lizzie Whittington, I can't answer your question because there is no question. But I can tell you something. Sometimes you have to think out of the box and answer the question, sometimes you don't fully understand the question, then you read the question again, again and again until you understand it. Which part of the equation do you times? Well sometimes it involves you reading in on perspective or another. Once you fully understand it, you can translate it into algebraic language.

You just need to understand what the question is saying(24 votes)

- I know how to do the math really well, but when it comes to word problems I get stuck and don't know what to do. Is there a specific method or any techniques I can do to set an equation or a word problem up?(20 votes)
- The trick with word problems is thinking, 'what is the question asking me?' 'What information do I have?' 'What information is relevant?' Look for key words which could relate to operations, I.e if the question asks about difference you'll probably need to subtract, etc. this is the basic premise I use to teach word problems. Look up Newman's Prompts. It's a series of questions to ask yourself to breakdown word problems.(33 votes)

- I cannot understand one of the practice questions:

"Micheal is 12 years older than Brandon. Seventeen years ago, he was 4 times as old as Brandon."

So I first did m=b+12, representing Micheal's Age. Then I wrote the equation m-17=4b, representing how 4 times Brandon's age was equal to Micheal's age 17 years ago. So, I plugged my m into the 2nd equation, and got this:

b+12-17=4b

-5=3b

b=-5/3

Obviously that's wrong, but I don't understand how I could have constructed the equation incorrectly.(8 votes)- The mistake is in your 2nd equation. Both people are 17 years younger. You only have Mike as 17 years younger.

Correct 2nd equation: m-17 = 4(b-17)

Hope this helps.(6 votes)

- how is this possibke(7 votes)
- Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I will be three times as old as you will be". Solve it algebraically...(5 votes)
- If A is Aftab and D is daughter, then A -7 = 7(D-7) and A+3 = 3(D + 3). Try to solve this system of equations. I assume the question is what are their ages now.(4 votes)

- I dont understand when sal says: We wanna solve for y, such that 18 plus y is going to be equal to 3 times, 2 plus y. Can someone explain and help me with this please {:((4 votes)
- 18 + y = 3 ( 2 + y ) : step 0, write out the equality

18 + y = 6 + 3y : step 1, apply the distributive property of multiplication

18 + y - y = 6 + 3y - y : step 2, subtract y from each side of the equation

18 = 6 + 2y. : step 2.5, the result of step 2

18 - 6 = 6 + 2y - 6 : step 3, subtract 6 from each side

12 = 2y : step 3.5, the result of step 3

Now, what' s the answer? I'm tired of typing!(4 votes)

- I literally am so confused. I have no idea how to do this and I don't even know what I don't know. Help please!(4 votes)
- You just need to assume the unknown as x. Then, try to build a linear equation. Try to solve that equation.(4 votes)

- Got no idea how to do these word problems.(5 votes)
- Try to think about the ages in the past and in the present. Then think about the time difference. What ever there ages are you can take that then add or subtract the time difference. Make sure to put this in brackets. Then multiply or divide or add or subtract based on the relationship between the two ages.(2 votes)

- * visible confusion *(5 votes)
- I did it a different way:

3(x+2) - 18 = x

3(x+2) is arman's age 'then'.

Diya is 2 now, so add some year 'x' and multiply by 3 will give armans age at the time. (I could write 2+x but it was just easier to write it as I did for me personally as I thought changing addition order will not change the sum)

I know Arman is 18 and therefore, the difference between his age then vs his age now will give the years between them i.e. the years it took.

But for some of the equation, I ended up with minuses so I wonder if my equation is still correct in terms of what I was trying to show?

3(x+2) - 18 = x

[multiply out the brackets]

3x + 6 - 18 = x

[Brackets multiplied]

+ 6 - 18 = - 2x

[minus 3x from both sides]

- 12 = - 2x

[divide by -2 from both sides]

6 = x(4 votes)

## 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 three
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 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 three times
as old as Diya? So let's set some variable--
let's say, y for 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 three times as old as Diya? Well, let's think about how
old Arman will be in y years. How old will he be? Let me write here. 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's
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 in y years? Well, she's 2 now,
and in y years, she will 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
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 3 times 2 plus y. Notice, this is
Arman in y years. This is Diya in y years. And we're saying that what
Arman's going to be in y years is three 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 the left hand
side-- and maybe I'll do this in a new
color, 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 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 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'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 going to 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. Two 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
one-coefficient year, we would divide
by 2 on the right. Whatever we do to one
side of an equation, we have to do it
on the other side. Otherwise, the equation will
not still be an equation. So we're 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
three 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 six years, how
old is Arman going to be? He's going to be 18 plus 6. We now know that
this thing is 6. So in six 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 8 years old. And lo and behold, 24 is,
indeed, three times as old as 8. In 6 years-- Arman
is 24, Diya is 8-- Arman is three times as
old as Diya, and we are done.