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(male narrator) In this video,
we will look at solving mixture problems
which use pure solutions.
The important thing to remember is that the percentage of acid--
or other chemical-- in pure acid will be 100%,
because it's pure acid, which as a decimal is 1.0.
If we're talking about water,
the percentage of acid-- or other chemical--in the water
will always be 0%, or as a decimal, just 0.
Let's take a look at some problems
where we have to use either pure acid--
or some other chemical-- or pure water.
In this mixture problem,
we need 1,425 milliliters of 10% acid.
The amount times the part is going to equal the final:
1,425 and 10% is what we want at the end.
Ten percent as a decimal is .1.
On hand, we have a 5% alcohol mixture.
As a decimal, that's .05.
And we have a pure alcohol mixture.
Pure alcohol will be 100%, or 1.0.
We don't know the individual amounts,
so we'll call them x and y.
We can now calculate our finals
by multiplying to get .05x, one y, and 142.5.
We can now get our equation from the last column:
.05x; plus y, the pure; equals 14...142.5.
The first column-- x plus y--equals 1,425.
This equation we can solve quite quickly
by using the addition method
and multiplying the second equation by -1
to eliminate the y's.
The first equation, unchanged, is .05x, plus y, equals 142.5.
The second equation: -x minus y; equals -1,425.
When we add those together, the y's eliminate,
and we get -.05x, equals negative...
whoops...actually, we get -.95x...
equals -1,282.5.
To get x alone, we simply divide both sides by -.95,
and we find out x--the amount of the first solution--is 1,350.
To find the second solution, we plug into the equation:
x, or 1,350; plus y; equals 1,425;
and subtract 1,350 from both sides;
and we find out y is 75.
x--the 1,350 milliliters-- is the 5%;
y--the 75 milliliters--is pure.
Let's take a look at another example
where we have to set up
this pure--either alcohol or water--situation.
In this problem...
we need 60% methane.
That's what we need at the end, .6.
We have on hand 180 milliliters--
the amount of 85%, .85.
We wanna know how much water-- don't know the amount,
but the percent in water is always 0--
will give us the desired solution.
We can calculate the total amount
by adding the 180, plus x,
and multiplying to get our finals:
180 times .85 is 153; x times 0 is just 0;
and .6, when distributed through,
will give us 108, plus .6x.
With only one variable,
we get our equation from the last column:
153 plus 0, we don't really need;
equals 108; plus .6x.
Subtract 108 from both sides, and we get 45 equals .6x.
Divide both sides by .6...
and we end up with x-- the amount to add--
is 75 milliliters of water.