Question 98236This question is from textbook Intermediate Algebra through Applications
: As part of a lab experiment for your chemistry class, you add pure alcohol to 24 ml of a 9% solution. How much pure alcohol must you add to the 9% solution to make a 16% solution?
My professor was showing us how to set up charts to help solve the problems and I don't know where to begin. I just need help setting up a chart and then I could solve the problem. -Thanks
This question is from textbook Intermediate Algebra through Applications
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! As part of a lab experiment for your chemistry class, you add pure alcohol to
24 ml of a 9% solution. How much pure alcohol must you add to the 9% solution
to make a 16% solution?
My professor was showing us how to set up charts to help solve the problems and
I don't know where to begin. I just need help setting up a chart and then I
could solve the problem. -Thanks
There are many ways to make a chart. Below is one way, but your professor
might use another one.
Think of each liquid as containing part alcohol and the rest water.
Let the 24 ml. of 9% solution be called the "first" liquid.
Let the pure alcohol be called the "second" liquid. When we
mix them we will call that the "final" liquid.
milliliters of mililiters of mililiters of
liquid alcohol water
First liquid
Second liquid
----------------------------------------------------------------
Final liquid
Let the number of milliliters of pure alcohol we need to add be x.
So let's place x for the number of milliliters of the second liquid.
milliliters of mililiters of mililiters of
liquid alcohol water
First liquid
Second liquid x
----------------------------------------------------------------
Final liquid
We are told we have 24 liters of the first liquid, so we fill
in 24 for the number of milliliters of the first liquid:
milliliters of mililiters of mililiters of
liquid alcohol water
First liquid 24
Second liquid x
----------------------------------------------------------------
Final liquid
Now we will figure how many milliliters of alcohol the first
liquid contains. Since it is 9% alcohol we multiply .09 by
24 and get 2.16 ml of alcohol in the first liquid, so we fill
in 2.16 for the number of milliliters of alcohol in the first liquid.
milliliters of mililiters of mililiters of
liquid alcohol water
First liquid 24 2.16
Second liquid x
----------------------------------------------------------------
Final liquid
The rest of the 24 milliliters is water, so we subtract 2.16 from
24 to get 21.84 milliliters of water. So we fill in 21.84 as the
number of milliliters of water in the first liquid.
milliliters of mililiters of mililiters of
liquid alcohol water
First liquid 24 2.16 21.84
Second liquid x
----------------------------------------------------------------
Final liquid
Next since the x milliliters of the second liquid is pure alcohol,
then it contains x milliliters of alcohol. So fill in x also for
the number of milliliters of alcohol in the second liquid
milliliters of mililiters of mililiters of
liquid alcohol water
First liquid 24 2.16 21.84
Second liquid x x
----------------------------------------------------------------
Final liquid
Now since there is no water in the second liquid (since it is all
pure alcohol) we enter zero for the number of milliliters of water
in the second liquid.
milliliters of mililiters of mililiters of
liquid alcohol water
First liquid 24 2.16 21.84
Second liquid x x 0.00
----------------------------------------------------------------
Final liquid
Now to get the total number of milliliters of the final liquid,
we add the 24 and the x and get 24+x, so we fill that in
for the number of millilters of liquid in the final liquid.
milliliters of mililiters of mililiters of
liquid alcohol water
First liquid 24 2.16 21.84
Second liquid x x 0.00
----------------------------------------------------------------
Final liquid 24+x
Now to get the total number of milliliters of alcohol in the final
liquid, we add the 2.16 and the x and get 2.16+x, so we fill that in
for the number of millilters of alcohol in the final liquid.
milliliters of mililiters of mililiters of
liquid alcohol water
First liquid 24 2.16 21.84
Second liquid x x 0.00
----------------------------------------------------------------
Final liquid 24+x 2.16+x
Now to get the total number of milliliters of water in the final
liquid, we add the 21.84 and the 0.00 and get 21.84, so we fill
that in for the number of millilters of alcohol in the final
liquid.
liquid alcohol water
First liquid 24 2.16 21.84
Second liquid x x 0.00
----------------------------------------------------------------
Final liquid 24+x 2.16+x 21.84
Now to get the equation, we reason this way:
The number of milliliters of alcohol in the final mixture is 16% of
the number of milliliters of liquid in the final mixture.
or
2.16+x is 16% of 24+x
"is" means "equals"
"16%" means ".16"
"of" means "times"
So the equation is
2.16+x = .16(24+x)
Solve that and get x = 2 milliliters of the second
liquid which is pure alcohol.
Notice that you don't really need to have the column
for the number of milliliters of water, for it doesn't
enter into the equation. However I included it in
order to break down the thinking process for you. You
may omit the "miililiters of water" column from your
work.
Edwin
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