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## Integrated math 1

### Course: Integrated math 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

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# Age word problem: Imran

Sal solves the following age word problem: In 40 years, Imran will be 11 times as old as he is right now. How old is he right now? Created by Sal Khan.

## Want to join the conversation?

- please someone help me....I am homeschooled and i don't know how to solve these questions....so please can someone tell me how to solve these questions..I will be really grantfull to you even if you just helped me out in only one question!!..thanks

1.Mary's age is 2/3 that of Peter's.Two years ago Mary's age was 1/2 of what Peter's age will be in 5 years' time.How old is Peter now?

2.A half of what John's age was 4 years ago is equal to one third of what it will be in 5 years' time.How old is John now?>>>thanks<<<(16 votes)- Define m as Mary's age, p as Peter's age, convert the problem into algebra notation.

1.Mary's age (m) is(=) 2/3 that of Peter's((2/3)*p).Two years ago Mary's age(m-2) was(=) 1/2 of what Peter's age will be in 5 years' time[(1/2)*(p+5)].How old is Peter now?

Get two equations...

m=(2/3)*p, and

(m-2)=(1/2)*(p+5), multiply 2nd eqn by 2 to eliminate fraction, so system is

m = (2/3) p

2m - 4 = p + 5, substitute value of m from 1st eqn into 2nd eqn, get

2((2/3)p) - 4 = p + 5, solve for p... simplify multiplication first

(4/3)p - 4 = p + 5, add 4 to both sides, get

(4/3)p = p + 9, subtract p from both sides, get

(1/3)p = 9, multiply both sides by 3 to eliminate fraction, get

p=27, Peter is 27 years old.

2.A half of what John's age was 4 years ago[(1/2)(j-4)] is(=) equal to one third of what it will be in 5 years' time[(1/3)(j+5)].How old is John now?

(1/2)(j-4) = (1/3)(j+5), I would multiply both sides by 6 to eliminate all the fractions... get

3(j-4) = 2(j+5), work through distributive property

3j - 12 = 2j + 10, add 12 to both sides

3j = 2j + 22, subtract 2j from both sides

j = 22(35 votes)

- I am having a lot of trouble solving these types of problems on the "Age word problem" questions. Could someone help me with this?

Here's an example:

Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel.

How old is Daniel now?(12 votes)- let k=kevins age now

let d=daniels age now

k=d+3, kevin is 3 yrs older than daniel now.

2 years ago, kevin was k-2 years old, daniel was d-2 years old, and kevin was 4 times daniels age:

(k-2)=4(d-2), which becomes k-2=4d-8 then k=4d-6. we also know k=d+3 since kevin is 3 years older than daniel now. if you substitute for k, then 4d-6=k=d+3.

4d-6=d+3, 3d=9, d=3.

daniel is 3 years old now.

hope this helps(21 votes)

- When viewing these videos in the 8th grade, "Systems of equations" playlist, the elimination method of solving a system of equations has not been introduced.

This is jarring. It would be nice if the elimination method was introduced earlier, or these videos just used the substitution method.(13 votes) - How do i solve this problem, please help

The sum of the ages of Jennie and Matt is 40. Jennie is 5 less than twice Matt's age. How old is Matt?(8 votes)- First, you would want to read it over and think of a way to convert this into an equation. so let's say Jennie's age is j and matt's age is m. Jennie's age is 5 less than twice matt's age so jenny's age(j)=2m-5. Jenny's and matt's ages add up to 40 so we know that jenny's age is

2m-5 and matt's age is m so 2m-5+m=40.

2m+m-5=40 lets get rid of the 5 so add 5 to both sides

2m+m=45

3m=45 (because 2m+m = 2m+1m=3m)

what times 3 is 45? divide both sides to find out

m=15 Matt is 15 years old. Jenny is 25.(5 votes)

- Kevin is 3years older than Daniel. Two years ago, Kevin was 4times as old as Daniel.

How old is Kevin now?(4 votes)- Well, to solve it logically, I would say, for Kevin’s age to be 4 times as much as Daniel, while the age difference is 3, is when Daniel is 1 years old and Kevin is 4. And so, Kevin’s current age is 4 + 2 which is 6.(4 votes)

- What happens if Imran dies in the next 40 years?(4 votes)
- Still dont get it.(3 votes)
- Hi everyone, may be I missed smth, but why, for instance, if somebody in 16 will be as 3 times older as he now, his age at this moment is 8 by an equation like this b+16=3b? If I've reached now eight years old, so, my age times 2 is sixteen, not times three. So, in 16 I'll be as 2 times older as I now. Right? Is in this case some mentality difference of understanding of English or problems of my math understanding?(2 votes)
- Sounds like the problem is asking you to compare your current age with your age 16 years into the future. You have the equation equation: b + 16 = 3b

b = your current age NOW, in 2018

In 16 years, your age becomes b+16

If your current age = 8, then in 16 years, your age = 8+16 = 24

Does 24 = 3 times your current age? Yes! 3*8 = 24.

In your analysis, you are only going 8 years into the future, not 16 years. The problem isn't saying your future age is 16, it is saying "your age in 16 years".(2 votes)

- I saw all of the age word problems. THEY ARE NOT SYSTEMS! They only use one equation. Not helpful!(2 votes)
- They are systems! You are probably making the equations wrong. Some, like this one, may only require one equation. In that case, make sure you have a variable to solve for. Some are more complicated and require 2 equations. For example, say David is 5 years younger than Savanna. In 7 years, David will be 3 times younger than Savanna. What is Savanna´s age? In these problems, one equation will NOT help you. Let D be David´s age and S be Savanna´s age. D+5=S, and D+7=3(S+7). That gives you a system of equations. Whenever you have more than one variable, you NEED to have the same number of equations as the number of variables (three different variables means you need three different equations). Otherwise, you cannot solve the system.(2 votes)

- i cant figure out this problem

Ben is 39 years old and Ishaan is 3 years old.

How many years will it take until Ben is only 4 times as old as Ishaan?(1 vote)- so some year in the future, Ben will be 39+x and Ishaan will be 3+x. We want the year when 39+x = 4(3+x), see if you can solve it.(4 votes)

## Video transcript

We're told that
in 40 years, Imran 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 encourage you
to try this on your own. Well, let's see if we can
set this up as an equation. So let's figure out what
our unknown is first. Well, our unknown is
how old he is right now. I'm just arbitrarily using x. We always like to use x. But I could've really
set it to be anything. But let's say x is equal
to how old he is right now. How old-- not how hold. 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 40 years Imran is
going to be x 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, 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, 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. 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 we avoid negative numbers,
let's stick all the x's here. So if I want to get rid of
this x on the right hand side, I'd want to subtract an x. But obviously, I can't
just do it to the right. Otherwise, the equality
won't be true anymore. I need to do it on
the left as well. And so I am left with--
if I have 11 of something and I take away 1 of them, I'm
left with 10 of that something. So I'm left with 10 times x is
equal to-- well, these x's, x minus x is just 0. 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 could have our drum roll now. We are left with x is
equal to 4 years old. x is equal to 4. So our answer to the question,
how old is Imran right now? He is 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. This is a factor of 11
years, so it all worked out.