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## Percentage word problems

## Video transcript

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 are the emperor
penguins, which are 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 is equal to 15. And now to solve this, we
just have to divide both sides by 0.30. So let's do that. 0.30, 0.30, we get x is
equal to 15 divided by 0.30. 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 could essentially multiply
both of these by 100. And when you multiply
both of them by 100, you can't just
multiply one of them. Then you would 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 over
two spots, so it becomes 1,500. So it really boils down
to how many times-- the same number of times that
30 goes into 1,500 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 1,500, 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 five times. 5 times 30 is 150. Subtract, you get 0. And then 30 goes
into 0 zero times. So this 30 goes into
1,500 fifty times. So this right over
here is equal to 50. And you can verify it. Multiply 0.3 times 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 15. You could say 15 over the
total number of penguins at the zoo is equal to 30%. Percent literally
means 30 hundreds. 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 you 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 are 50.