SOLUTION: A mixture of 6% disinfectant solution is to be made from 7% and 3% disinfectant solutions. How much of each solution should be used if 32 gallons of 6% solution are needed?

Question 585245: A mixture of 6% disinfectant solution is to be made from 7% and 3% disinfectant solutions. How much of each solution should be used if 32 gallons of 6% solution are needed?
Found 5 solutions by sofiyac, amalm06, ikleyn, MathTherapy, greenestamps:
Answer by sofiyac(983)   (Show Source): You can put this solution on YOUR website!
If end result is 32 gallons then if we say we need x gallons of 7% solution it would mean we would need 32-x gallons of 3% solution
percent1*volume1+percent2*volume2=finalpercent*totalvolume
7x+3(32-x)=6(32)
7x+96-3x=192
4x+96=192
4x=96
x=24
so we need 24 gallons of 7% solution and 32-24=8 gallons of 3% solution
Answer by amalm06(224)   (Show Source): You can put this solution on YOUR website!
Using the method of alligation,
0.06-0.03=0.03 and 0.07-0.06=0.01
So that 0.01/0.03=1/3
Then 32*(1/4)=8 gallons of 3% solution (Answer)
32-8=24 gallons of 7% solution (Answer)
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Dear tutor @amalm !

If you will teach students to solve such problems in this way,

they, probably, will be able to calculate quickly,

but definitely will know NOTHING and will understand NOTHING about what they are doing and what their calculations mean.

And will, actually, know NOTHING about what the REAL solution really is.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

A mixture of 6% disinfectant solution is to be made from 7% and 3% disinfectant solutions. How much of each solution should be used if 32 gallons of 6% solution are needed?

Let amount of 7% solution to mix, be S
Then amount of 3% solution to mix is, 32 - S
We then get: .07S + .03(32 - S) = .06(32)
.07S + .96 - .03S = 1.92
.07S - .03S = 1.92 - .96
.04S = .96
S, or amount of 7% solution to mix is:
Amount of 3% solution to mix is:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Dear tutor ikleyn:

What's wrong with being able to calculate quickly?! In many of your responses to questions on this web site, you mock the writer by saying that by using a particular method you can get an answer in a few seconds.

If you "scold" students for using slow methods when a faster method is possible, then why do you scold another tutor who offers a faster way to solve this kind of problem?

Just because you can't understand how the method of alligation works doesn't mean it shouldn't be taught.

The method of alligation is far more efficient than the traditional algebraic approach that you and most other people use. In this problem, finding the answer is almost trivial:

6% is 3 times as close to 7% as it is to 3%; therefore the mixture should contain 3 times as much of the 7% ingredient as it does of the 3% ingredient.
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