Today you got to pretend to be chemists, which is kind of fun. How many milliliters, ml stands for milliliters, notice that the m is small the L is capital okay, side track. How many milliliters of a 50% alcohol solution must be mixed with 1mL of a 10% alcohol solution to get a 46% alcohol solution?
Okay that one is really tricky but so what we are going to do is try to use that equation where we are going to have amount of ingredient 1 times it’s concentration plus amount of ingredient 2 times it’s concentration is going to be equal to my mixture amount times my mixture concentration.
Okay here we go conc. you get the idea let's do it. The amount times the concentration of my first ingredient well my first ingredient it says how many milliliters that means I got to know the mL. I'm going to call it x of 50% alcohol solution, okay that's the concentration I’m going to write it as .50 for 50%.
Next I’m going to be adding or mixing with it 1 mL over 10% alcohol solution. So I’m going to write my amount is 1 my percent is 10 that's going to be equal to my mixture amount what's my mixture amount? That's tricky my mixture amount I’m combining ingredient 1 and ingredient 2 so to write my mixture amount I’m going to do amount of 1, ingredient 1 plus amount of ingredient 2. That was tricky let me tell you again what I did.
For my mixture amount I know I’m combining two things here is the first thing that is the amount of it, here is the second thing that's the amount of it so my two amounts together is how much I have of my mixture.
Last thing I have to multiply that by my concentration of the mixture .46. Setting up the equation is the most difficult part but once you do this its just plugging chugging, happy solving be careful because you have Xs on both sides of the equal sign and you are going to need to distribute.
So here we go .5x plus that's just point 1 when I multiplied out is equal to 2 distribute .46x plus .46, to get all of your Xs on the same side of the equal sign I’m going to subtract .46x from both sides sorry guys I hope you can see my decimal points.
Subtract it and so I get .04x plus .1 is equal to .46 subtract point 1 from both sides and I’ll have .04x is equal to point 36. Last but not least divide both sides by .04, I’m going to grab my calculator.
.36 divided by .04 is 9.That tells me x equals 9 but what does 9 mean be sure to label with units x represents the amount of my 50% solution. So when it said how many milliliters is 50% solution I’m going to say 9 milliliters of the 50% alcohol solution.
Before we even move on to the next problem make sure your answer makes sense logically think about how I have like half percent alcohol plus 10% alcohol this guy is much stronger, so I’m probably going to be putting in a good amount to keep my concentration pretty close to half.
Looking at these numbers tells me that I’m going to be adding proportionally more of these 50% guy compared to this 10% guy because I want to keep the concentration pretty strong. So when I look at 9 milliliters it is a lot more than 1. So that makes sense as far as what I got for my answer. So again guys you can do these problems don't just skip them pretend like you are a chemist, buckle down, it’s a process, it’s a journey but you can do it and use this formula to get you guys set up from there it’s just easy solving.
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M.A. in Secondary Mathematics, Stanford University B.S., Stanford University
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