Algebra 31 - Calculating Mixtures of Solutions

This lecture shows how Algebra is used to solve problems involving mixtures of solutions of different concentrations.

[deaftodd]

Now I have solved my hand sanitizer solution.

[hctiBelttiL]

Regarding the last problem, you could just think of the percentages as subunitary values (values between 0 and 1).
Refactoring it as such:

10*0.05=0.12x+0.02y

y=10-x

0.5=0.12x+0.02(10-x)

0.5=0.12x+0.02*10-0.02x

0.5=0.12x+0.2-0.02x

0.3=0.12x-0.02x

0.3=(0.12-0.02)x

0.3=0.1x

(0.3=0.1x)*10

3=x

x=3

y=10-3

y=7

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profit.

I find that to be a way simpler way to think about it. Also, I don't like "cancelling out" stuff, it often leads to mistakes. Also also, I think fractions are silly. Fight me. I dare you.

[corygillis]

This is a great video! Thank you for such detailed info. But I arrived at an answer that still didn't solve my problem. I have 57oz at 35% and 128oz at 77%. I need 100oz at 50%. What strength should I cut the 77% down to, to make 100oz at 50% by adding it to the 57oz of 35%? Do you have any videos about this? I believe the only difference between this video and the one I need is that I have predetermined volumes.

[Fan]

Awesome videos. Your videos have helped me understand Algebra much better. I was wondering if in the future you can make video for Calculus.

[igetnoviews]

Thank you. I was looking for this kind of explanation all day

[pkkhuni]

You make algebra interesting for children

[MegaMementoMori]

I don't really understand why can't you just divide (solution/solute) instead of (solute/solution)x100? It saves one step.

[timkingston]

Hi, thanks so much for your helpful videos. Could you please recommend some books to practice real-world algebra problems, such as those you present here? (I saw this question answered in another comment, but I can’t find it. Apologies for the repetition!)

[spacemanduke]

Can you show how to mix solutions using multiple solutes? For example, suppose I want to make my special red lemonade that has x amount of sugar, y amount of pulp, and z amount of red food coloring. I have two mixtures of red lemonade already but they aren't my special mixture. One mixture is too high in all three solutes and the other is too low in all three. How will this problem be set up?

[Golden_Tortoise]

at 8:00 I understand how the equation works, but I don't understand how can someone know to to used 5 instead of .05 since its a percent after all. In the table, the 12% and 2% was converted into .12 and .02, so I would think the 5 would be converted into .05 as well.

[mrshrums]

MyWhyU i subscribed and thanks for your vids

[tiredpoe]

I would like to know more about why it's "10-X". Is it because it's 10% less concentration? And if there isn't a value for the total volume needed then what would I do then?

[jasmus]

Algebra was never my strength, so I am learning the bits I should have mastered earlier. Just sent it to my two sons for comment (one a data base admin, and other other is doing maps for Apple).

[jromeroevo]

And the teachers don't teach like this because? lol