Let's look at how we can use linear equations to help us solve mixing

problems. For example a student is mixing 2

solutions that contain hydrogen chloride. The first solution is 15% hydrogen

chloride, and the second is 5% hydrogen chloride.

How many milliliters of each solution should the student mix in order to obtain

100 milliliters of an 8% hydrogen chloride solution? Alright so this

student has a solution, that is 15% hydrogen chloride, which is being mixed

with a solution, that is 5% hydrogen chloride to produce a solution, that is

8% hydrogen chloride. Alright so let's let x equal the number

of milliliters, of the 15% solution that the student will mix and y equal the

number of milliliters of the 5% solution. And therefore, x+y will equal the number

of milliliters of the 8% solution. However, looking back up here, no

problem. We know how many mm it has to be.; It has

to be 100. which means x+y=100.

Or y=100-x. So let's write that up here.

We're mixing x milliliters of the 15% solution with y or 100 - x milliliters.

of the 5% solution, to obtain 100 ml of a 8% hydrogen chloride(HCL) solution.

Now what's important to realize here is that the amounts,of HCL Before mixing is

equal to the amount of hydrogen chloride after mixing.

We do not create more hydrogen chloride by mixing.

[SOUND] Now what is the amount of hydrogen chloride before mixing? Well,

what is the amount of hydrogen chloride in the first solution here? Well, if

there is X milliliters of this solution, 15 percent of which is hydrogen chloride,

then the amount of hydrogen chloride in this first solution is point 1.5.

Times X. And then plus the amount of hydrogen

chloride in the 2nd solution, which is .05 times 100 minus x.

And this has to be equal to the amount of hyrdrogen chloride.

After mixing. Or .08 times 100.

So now let's solve this linear equation for X.

We have .15 times X plus, and distributing the .05 to both of these two

terms Gives us .05 times one hundred which is five and then minus .05 times x

is equal to .08 times hundred which is eight and combining the x terms on the

left hand side and bringing the five to the right hand side.

Give us 10* x = 3.. And now, dividing both sides by .10 gives

us x=30. And if x=30, we can plug that in over

here. Which gives us y=100-30 or 70.

And therefore, writing our answer up here, the student would need to mix x or

30 mL of the 15% solution. With y or 70 millilitres of the 5 percent

solution. In order to obtain.

100 Milliliters of the 8% hydrogen chloride solution.

So this would be our answer here. And this is how we can use linear

equations to help us solve mixture problems.

Thank you, and see you next time.

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