>> Math is cool and you can do it.
>> Alright, we are going to work through this percent mixture problem.
We have 10 quarts of pure apple juice added to 90 quarts of a fruit juice
that is 10% pure apple juice, what is the percent concentration
of pure apple juice in the resulting mixture.
So, the picture is we have some juice, some containers of juice, three containers
and we are mixing some pure apple juice with some other fruit juice that is only 10% apple
and we are going to get the resulting mixture.
So, we fill in what we know.
We have got 10 quarts of pure juice, so we know that there are 10 quarts here.
We have got 90 quarts of a juice that is 10% pure apple juice, so we know this is 90 quarts.
So, if we are mixing 10 quarts with 90 quarts,
how many quarts were there in the mixture, 100 quarts.
Alright, but it's asking us about the percent concentration,
in other words right here we do not know what percent this is
in the mixture of pure apple juice.
And also when it says pure apple juice it did not give us the percent at all,
so we have to think about what that means.
What does it mean to be pure apple juice?
That means it is all apple juice, 100% so pure means 100% and how do you write 100%
as just a number, it is 1, right?
You could do it by moving a decimal two places to the right or 100% equals 1.
How about 10%, how do you write 10% as a decimal, 0.1 or 0.10
and we do not know what this percent is, so I am going to call it p, alright?
So, we are going to have to figure out what p is and then write it as a percent.
So, now let us go and see how much pure apple juice is in each of these containers.
Well, we started out with 10 quarts and it was all pure, so we know it is 10
and of course you could get that by saying 10 times 1 right?
But this is going to be the pure apple juice in each.
And here we have got point 1 times 90, basically 10% of 90 and what would
that be, 10% of 90, that would be 9.
If you want you could first write 0.1 times 9 but that is going to equal 9.
And what we know is how to get always how much of the pure juice
is you take the percent times how much of the stuff you have, so that is p times 100
or 100 times p. And the amount of pure apple juice I have that I am putting in both
of these containers should still be the amount of pure apple juice that is in the final mixture.
So, we want there is our equation which we could simplify a little bit if you wanted
to write 10 plus 9 equals 100p, okay.
Alright, so this is not too difficult to solve, is it?
10 plus 9 is just 19 equals 100p, and we are trying to solve for p
so we have to divide both sides by 100.
Now, I want to write that as p equals nineteen hundredths.
Now, notice that is not a percent, nineteen hundredths though means 19%
and if you did not know that you could say, well to change any number
to a percent you multiply by 100%.
This is sort of pre-algebra material, that part having to change a fraction to a percent,
you just multiply it by a 100% and then what happens is the 100s cancel out and p is 19%,
so that is what we are looking for.
What is the percent in the resulting mixture should be 19%, so looks like that is 19%.
We could check it though.
So, here is how we check it, we go back and draw the picture.
Remember we already knew these first two things.
We had 100% of the 10 quarts of the pure apple juice and we had 90 quarts
of the 10% apple juice, and the [inaudible] that was a 100 in here so we just found
out that this was 19%, so now I am putting in the 19%.
So, this is what I am checking and I am making sure this is really correct, okay?
So let us see, we had also figured this out previously, 100% of 10 is just 10
and 10% of 90 is just 9, and is that the same thing as 19% of 100, well 19% of 100 is 19.
Is this true that 10 plus 9 equals 19, that is what you want to find out.
This is the amount of pure apple juice in the first container, the amount of pure apple juice
in the second container is that the same thing
as how much pure apple juice there is in the mixture, and it is.
So then the question is what is the resulting percent?
And we want to answer in words because this is a word problem you do not
like x equals 0.19 or 19%.
There was no x. It was a word problem, so the resulting percent...
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>> In the final mixture...
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>> Was or is 19%.
And there is another percent mixture problem where this time you did not know the percent.
>> I hope you learn something, remember math is cool.