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## Systems of equations word problems

# Age word problem: Imran

CCSS.Math: , , , ,

## 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.