SOLUTION: You need to strengthen a 22% alcohol solution with a pure alcohol solution to obtain a 70% solution. How much pure alcohol should you add to 100 milliliters of the 22% solution?

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Question 1203535: You need to strengthen a 22% alcohol solution with a pure alcohol solution to obtain a 70% solution. How much pure alcohol should you add to 100 milliliters of the 22% solution?
Found 3 solutions by Theo, greenestamps, josgarithmetic:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
.22x + y = .70 (x + y)
this becomes .22x + y = .70x + .70y
subract .70y from both sides of the equation and subtract .22x from both sides of the equation to get:
.30y = .48x
you are given that x = 100, therefore:
.30y = .48 * 100.
this becomes .30y = 48
solve for y to get y = 48/.30 = 160
you have x = 100 and y = 160 for a total of x + y = 260.
you take 22% of of x and 100% of y to get .22 * 100 + 160 = 182 milliliters of alcohol in a solution that totals 260 millliliters.
the ratio of alcohol to solution is 182 / 260 = .7 whch is 70%, as desired.
your solution is that you have to add 182 liters of pure alcohol to a 22% solution of alcohol to get a 70% solution of alcohol.

x was the number of liters of 22% alcohol solution.
y was the number of liters of 100% alcohol solution.
x + y was the total solution.


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The standard algebraic solution looks something like this:

100 ml of 22% alcohol, plus x ml of 100% alcohol, yields (100+x) ml of 70% alcohol.

.22%28100%29%2B1.00%28x%29=.70%28100%2Bx%29
22%2Bx=70%2B.7x
.3x=48
x=48%2F.3=160

ANSWER: 160 ml

Here is an alternative, informal method which often makes reaching the answer easier.

Picture a number line showing the three percentages -- 22, 70, and 100. Calculate that 70 is 48/78 of the way from 22 to 100 (22 to 70 is a difference of 48; 22 to 100 is a difference of 78).

That fraction 48/78 means the two ingredients must be mixed in the ratio 48:(78-48) = 48:30 = 8:5. Since 70% is closer to 100% than to 22%, the larger portion must be the 100% alcohol. Then we have the proportion

8%3A5=x%3A100
5x=800
x=160

And again of course the answer is 160 ml.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The problem can be done all in variables, but seems easier to handle using a table of data.
MATERIAL CONC.%         VOLUME         AMOUNT PURE
         22              100             22*100
        100               v              100v
         70              v+100           70(v+100)

Question asks for how much of the pure 100% alcohol to add, v.

Accounting for the amount of alcohol for the separate parts,
100v%2B22%2A100=70%28v%2B100%29

100v%2B22%2A100=70v%2B70%2A100
%28100-70%29v=70%2A100-22%2A100
v=100%28%2870-22%29%2F%28100-70%29%29-------simplify and compute.
v=100%2848%2F30%29
v=100%281.6%29
highlight%28v=160%29---------ml. of the pure 100% alcohol to use