Welcome to the presentation on age word problems.
Let's get started.
Well, I already have one written down here.
It says in 4 years, Ali will be 3 times as old as he is today.
How old is Ali today?
Well, let's just say that x -- that's a little too big for
what I want to write -- x equals Ali's current age.
Or his age today.
Please forgive my handwriting.
If x is Ali's current age -- and here we say, in 4 years.
So how old is Ali going to be in 4 years?
Well, if x is his current age, in 4 years, he's going to
be x plus 4 years old.
So that is equal to Ali's age in 4 years.
Let's read what other information there
is in the problem.
It says, in 4 years.
So in this situation, that's a 4, x plus 4, in 4 years
Ali will be 3 times as old as he is today.
Well, today he's x.
So we say, in 4 years.
x plus 4.
And that's just -- so, in 4 years.
So we could translate that into x plus 4.
That's going to equal 3 times as old as he is today.
Well, we know today he's x.
So that's going to be equal to 3x.
And now we just solve for x.
Subtract x from both sides.
You get 2x is equal to 4.
x equals 2.
So Ali is 2 years old today.
Let's do another problem.
That makes sense, because if he's 2 today, in 4 years
he's going to be 6.
Which is going to be 3 times as old as he is today.
So it all works out.
Let's do another problem.
Let's clear this and now I'm going to attempt to type.
Hope I don't mess up.
OK.
The problem, is Nazrith is 4 years older then Omama.
2 years ago, Nazrith was 5 times as old as Omama.
How old is Nazrith today?
This one seems more difficult.
But I think we'll be able to get through it.
Let's figure it out.
All right, so once again what are we trying to solve for.
We're trying to solve for Nazrith today.
So, let's say this is Nazrith.
We'll say Naz for short.
And let's say this is Omama.
And this is today.
I'm making a little chart.
And let's say 4 years from now.
4 -- oh, no, no.
Not 4 years from now.
I'm confusing myself.
This would be 2 years ago.
I'm still remembering the last problem.
2 years ago.
So this is today, 2 years into the future.
Let me make a little chart.
It's not the cleanest chart, but I think it'll do the job.
So we're trying to solve for x.
How old is Nazrith today.
So let's just say Naz today that is equal to x.
It says Nazrith is 4 years older than Omama.
So this piece of information up here-- let me underline it.
Nazrith is 4 years older Omama.
Well, that piece of information tells us that Omama today, if
Nazrith is x, then Omama's going to be x minus 4.
Which makes sense because Naz is 4 years older than Omama.
Now we go into the past.
Let's write like this.
So, 2 years ago -- so if Naz is x today, how old
was she 2 years ago?
Well, she was going to be x minus 2.
That makes sense.
If I'm 10 years old today, 2 years ago,
I'll be 2 years less.
I'd be 8 years old.
So, if she's x today, 2 years ago she was x minus 2.
And if Omama is x minus 4 today, than 2 years ago
she'll be 2 less than that.
So she'll be x minus 4 minus 2.
And that equals x minus 6.
Which makes sense.
And, notice that she's still 4 years younger
than Naz, or Nazrith.
Now we have one final piece of information in this problem.
It says, 2 years ago Nazrith was 5 times as old as Omama.
So, we're in this situation.
2 years ago -- that's what the sentence says, 2, years ago, so
it's this situation -- Nazrith was 5 times as old as Omama.
So Nazrith, which is x minus 2, was 5 times older than
Omama, which is x minus 6.
So let's just write that down.
So, Nazrith, 2 years ago, was x minus 2.
We get that from the chart.
Nazrith was x minus 2, 2 years ago.
And that sentence tells us, Nazrith was 5 times older
than Omama was 2 years ago.
Omama, 2 years ago, was x minus 6.
Well, now we just solve for x.
x minus 2 is equal to 5x minus 30.
Now we could subtract x from both sides.
And if you get 4x, I'm going to switch it around, to
hopefully confuse you more.
4x minus 30 equals minus 2.
And then we get 4x is equal to 28 and x is equal to 7.
So we solve the problem.
Nazrith, today is 7 years old.
And does this make sense?
Well, if Nazrith today is 7 years old, then Omama today
is going to be 3 years old.
And that makes sense, because there's a 4 year difference.
2 years ago, Nazrith was 5 years old.
And 2 years ago Omama was only 1 year old.
Because x minus 6.
So it makes sense.
Nazrith is 4 years older than Omama; Nazrith is
7, Omama is 3 right now.
2 years ago, when Nazrith was 5 times as old as Omama.
2 years ago, Nazrith was 5 and Omama was 1.
So it all works out.
Pretty deep, no?
Well, anyway, I think you're ready to at least try some
of these age problems.
And I'm going to do some more example problems.
So that you can come back to this video page and see
more if you're still a little bit confused.
Have fun.