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This video is provided as supplementary material
for courses taught at Howard Community College and in this video
I want to show how to solve some word problems involving percent.
So here's the first problem. Andy has 240 toy cars.
20 percent of the cars are red. How many red cars are there?
So the unknown in this problem
is the number of red cars that we're looking for. We'll use an
x to represent that number, and I'm going to make that x the numerator a fraction.
The denominator is going to be the total number of
toy cars - 240. So we've got this fraction, or ratio,
and I'm going to set that equal to the percent.
I've got 20 percent, but instead of writing
that as a percent, I'm gong to write it as a fraction. So I'll write the 20,
and instead of a percent sign, I'll put that 20 over 100.
So now I've got two fractions that create an equation -
x over 240 equals 20 over 100.
The first thing I want to do to solve this is get the x by itself,
which means getting rid of the 240 in this denominator.
So I'll do that by multiplying both sides
by 240. On the left side
the 240 will cancel out and all I'll have is x,
and on the right side of the equation I'll have to multiply 20 times 240.
Well 2 times 24 is 48,
and then I'll add two more zeros for each of the
zeros that had in those numbers.
And I've got to divide that by 100. That's going to mean
that I have x equal to 48.
That's going to be a number of red cars.
So let's just review this and then go on to one more.
I started out by making a fraction,
a ratio. I took the number of
red cars as the numerator. We didn't know what that was,
so I just used an x for that. The denominator was the total number
of cars.
I set that equal to the percent that I had, but I wrote the percent as a fraction.
So I had x over 240 equals
20 over 100, and then all I had to do
was solve that equation to find out what x was
and I got the number of red cars.
Let's try one more. If a bicycle that normally sells for $495
is on sale for 10 percent off, how much will it cost?
Well, we've got to do this problem in two steps. First we've gotta find out
how much 10 percent of 495 is.
That's going to be the discount, the amount that's subtracted
from the original price. And then what we do is
subtract that 10 percent - whatever number we find - from the original price,
and that will tell us the sale price.
So we'll start out by finding out how much the discount was.
We'll call that x - that's the 10 percent that's taken off.
And that will be the numerator
of the fraction. The denominator will be the original price 495.
We'll take that fraction, or ratio,
and set it equal to the percent, which was 10 percent.
I'm going to write that 10 percent as a fraction,
10 over 100. I want to solve for x,
which means I want to get x all by itself.
I'll multiply both sides by 495.
The 495 on the
left side will cancel out and I'll just have x.
Now I've got work on that fraction on the right. So I've got 10 times 495 -
thats 4,950.
I want to divide that by 100.
So all I have to do is take the decimal point at the end
of 4,950 -- there would be a decimal point there --
move it two places to the left and that would divide it by 100.
So I'm going to have x equals
$49.50. So that's the discount.
$49.50. So that's the discount.
Now we want to
subtract that number from the original price.
The original price was $495.
and the discount,
the amount I'm subtracting, is $49.50.
So let's do this subtraction.
Zero from zero is zero. I want to subtract
5 from the zero, which means I have to borrow a one.
So the 5 over here becomes a 4, and the zero becomes a 10.
5 from 10 is 5. I need to subtract 9 from 4, so once again I'll have to
borrow.
I'll take the 9 and turn it into an 8. The 4 becomes 14.
9 from 14 is 5.
Then I've got 4 from 8. That's 4. I'll bring down the last 4
and the final price for the bike is going to be
$445.50.
Okay, so I hope this helps. Take care,
I'll see you next time.