Tip:
Highlight text to annotate it
X
A zoo has 15 Emperor Penguins who make up
30% of the total number of penguins at the zoo.
How many penguins live at the zoo?
So let's let x equal the total number of penguins
who live at the zoo.
So, they're telling us that 30% of that [number]
are the emperor penguins – which is 15.
So they're saying, if we take 30% –
So 30% of x is equal to 15.
Or another way of saying this is
we could say – instead of writing 30%,
we could write that as a decimal –
as 0.30 of x.
So it’s 0.30 times x = 15.
And now, to solve this, we just have to divide
both sides by 0.30.
Let's do that.
[WRITES '0.30' TWICE.]
We get x is equal to 15/0.30.
Now that’s –
Let's do a little –
We’re going to have to do a little arithmetic
to solve this one.
So if we take 0 –
It's 15 divided by 0.30.
So just as a refresher of dividing decimals,
we can essentially multiply both of these by 100.
And when you multiply both of them by 100,
you can’t just multiply one of them,
[because] then you'd get a different answer.
But if you multiply both of them by 100,
you move this decimal point over two spots,
so it becomes a 30 –
And you move this decimal point over two spots –
so it becomes 1500.
So it really boils down to the fact that
the same number of times that 30 goes into 1500
is the number of times that 0.30 will go into 15.
So let's think about this.
(Let me rewrite it here, just so it’s neat.)
30 goes into 1500 –
All we did is we moved both decimals
over to the right, twice.
Or you could say, we just multiplied
the numerator and the denominator here by 100 –
which wouldn't change the value of the fraction.
So 30 goes into –
Let’s see. It doesn't go into 1. It doesn't go into 15.
It does go into 150.
It goes into 150 5 times.
5 × 30 = 150.
Subtract, you get 0.
And then 30 goes into 0 times.
So this 30 goes into 1500 fifty times.
So this right over here is equal to 50.
And you can verify it.
Multiply 0.3 × 50, and you will get 15.
Now there is another way of doing it.
You could say the fraction of Emperor penguins
over the total number of penguins at the zoo –
So you could say –
You could say 15 –
You could say 15
over the total number of penguins at the zoo
is equal to 30%.
Percent literally means 30 100ths.
So it’s equal to 30 for every 100.
It's equal to 30 for every 100.
And then you could solve for this right over here.
And a really simple way of doing this is to say,
“Look, to go from 30 to 15, you have to divide by 2 –
if you're going from the right to the left.
So let's divide by 2 right over here.
So x would be equal to 50.
15/50 is the same thing as 30/100.
So the total number of penguins is 50.