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# Combining mixtures example

Figure out how much of two gasoline mixtures to combine to get gasoline with a certain concentration of ethanol. Created by Sal Khan.

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• Not sure why these problems always throw me for a loop but, in case you get confused, here's a shorthand version:

``where c = content / v = volume / c3 is the total content / v3 is v1+v2c1(v1) + c2(v2) = c3(v3)``

This is just an abbreviated version of cancelling the denominator out and multiplying by the ethanol content

``18(30) + 25(v) = 20(30 + v)540 + 25v = 20(30 + v)25v-20v2 = 600-5405v = 60v=12``
• i don't understand this topic at all, i don't know if it needs any background information, if I need please tell me which lessons I should watch.
• why bring chemistry into pre-calc :(
• this is not chemistry
(1 vote)
• I didn't know the formula for concentration!
• Might be helpful to use the c1v1 + c2v2 =c3v3 formula where
c1 = .18, v1 =30, c2 = .25, v2 is unknown, c3 = .20 and v3= (30 + v2).
• Isn't this the acid-base titration equation?
• To verify the concentration, let's model the equation.
``target concentration = original ethanol volume + new ethanol volume / (original total volume + new total volume)``

Translate the equation into the given numbers, where v equals the new volume.
``target concentration = 5.4 + 0.25v / (30 + v)target concentration = 5.4 + 0.25(12) / [30 + (12)]``

The target concentration equals 0.20 which proves our new volume is correct.
• I made short summary of how to solve this problem using Sal's method.(And expanded the parts he skipped)
concentration=volume of ethanol/ total volume

>The tank originally has: 30L with 18% conc. ethnal
>Fuel station has: 25% conc gas [conc=vol eth./ total vol]
>We are asked to find how much we need to add to make it 20% conc
.

18%=vol. eth/30L vol. eth= 18%x 30L=5.4L

20%=New vol eth./ new total vol.

Let
`v= volume of gas we need to add (from the fuel station)x= volume of ethanol of the gas we need (from the fuel station`
`)`

conc=vol eth./ total vol

20%=5.4+x/ 30+v

conc of the gas (from the fuel station)= 25%=x /v

x=25%*v (substitute back

20%=5.4+25%v/ 30+v
0.2=5.4+0.25v/30+v
0.2(30+v)=5.4+0.25v
6+0.2v=5.4+0.25v
0.6=0.05v v= 0.6/0.05
v=12

volume of gas we need to add (from the fuel station) is 12 liters(L)

Hope this helps
• The Wording of this problem makes it seem like the Tank has a maximum capacity of 30L. It has taken an embarrassing amount of time to realize that is not what the sentence is saying. At the same time I would argue it is poorly worded. The Solve seems impossible if given just the max capacity and not the actual volume of gasoline in the tank.
• Yeah, I had the same issue.

I'm not native english speaker and I misunderstood the word "holds", because I associate it to capacity.

So my brain instantly reworded it as "A tank that holds 30L, is partially filled with gasoline with a 18% concentration of ethanol"