00:01
Here we have a mixture type of problem where we are combining two different types of candy.
00:07
They have different values.
00:09
And we would like to obtain a mixture that is seven pounds.
00:14
And it should sell for 96 cents per pound.
00:19
Okay.
00:20
So i drew a little diagram here to help us conceptualize what is going on.
00:24
We have some blue candy, red candy.
00:28
They're both on scales.
00:29
We don't know how much of them we need, but we do know that their mixture, when we have them combined, we would like to have seven pounds altogether.
00:40
So i'm going to rate seven pounds here.
00:43
Now, because we don't know the weights of the blue candy and the red candy, this is where we can introduce some variables.
00:50
We can introduce an x here and a y here.
00:54
However, i am going to try to make it so that i don't have two variables like this.
00:59
It will make it a lot easier.
01:00
If we don't.
01:02
So instead of a y, i'm going to get rid of that, i'm going to write something else here.
01:07
I'm going to use the fact that x plus whatever the weight is for the red candy, whatever that is, x plus that blank is equal to seven.
01:18
So in other words, x plus the remainder after you take away x from seven, that should give you seven altogether.
01:27
So what we should write here is seven minus x and that's going to be how much the of the red candy we'd like to have in pounds.
01:38
Okay, so these are both in pounds.
01:43
Again, if you're not sure why i wrote 7 minus x, maybe one thing that you can double check is, does x plus 7 minus x does it equal to 7? and i think once you check that, you'll be convinced, yeah, that makes sense.
01:59
Okay, so now that we have that, we have the weights.
02:04
We can focus on more of the costs.
02:07
So the costs for all of this.
02:09
Let's work with the right -hand side first.
02:12
The cost is going to be, well, there's seven pounds, and this mixture should be valued at 96 cents per pound.
02:20
So let's do, i'm going to write it this way, $0 .96.
02:27
So $0 .96 times.
02:30
7.
02:31
So that should give us the dollar amount of the mixture.
02:36
Now if we have what it should cost, we'll take the individual cost for the the blue candy and then how much the red candy costs add them together and that should equal 0 .96 times 7.
02:50
So the cost for the blue candy is 0 .81 times x and the cost for the red candy is 1 .28 times x and the cost for the red candy is 1 .28 times 7 minus x, which we need to write in parentheses.
03:07
And don't forget we are adding them together.
03:10
So this right here is the primary equation that we need to solve.
03:16
This is the 0 .81x plus 1 .28 times 7 minus x equals 0 .96 times 7.
03:26
Now a lot of people, including myself, don't like working with decimals.
03:30
So one thing that you can do to get rid of the decimals is to multiply both sides of this equation by 100.
03:41
So let me write that down.
03:43
100 and then 100.
03:48
You have to be careful when you're doing this, so.
03:52
So why do we do that? if you multiply 100 with 0 .81, essentially the decimal moves two places to write, and we just get 81, a nice whole number.
04:04
Same thing with the 1 .28...