Question 1159822: A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is
30
%
salt and Solution B is
80
%
salt. She wants to obtain
50
ounces of a mixture that is
40
%
salt. How many ounces of each solution should she use?
Found 2 solutions by greenestamps, Alan3354:
Answer by greenestamps(13215)   (Show Source):
You can put this solution on YOUR website!
You might get some responses saying that the problem is not possible because a salt solution can't be 30% or 80% salt. But since this is a forum for math questions, I will simply treat it as a math problem and ignore the fact that the problem as given is physically impossible.
The traditional algebraic method for solving the problem will start something like this....
let x be the number of ounces of 30% salt
then 50-x is the number of ounces of 80% salt
Then the equation to be solved relates the amounts of salt in the two ingredients and in the mixture. It says "30% of x ounces, plus 80% of (50-x) ounces, equals 40% of 50 ounces":
Solve the equation using basic algebra; I leave that to you.
If a formal algebraic solution is not required, here is a quick and easy way to solve "mixture" problems like this.
The ratio in which the two ingredients must be mixed is exactly determined by where the percentage of the mixture lies between the percentages of the two ingredients.
(1) 40% is 1/5 of the way from 30% to 80%. (30 to 80 is a difference of 50; 30 to 40 is a difference of 10; 10/50 = 1/5.)
(2) That means 1/5 of the mixture has to be the higher percentage ingredient.
ANSWER: 1/5 of 50 ounces, or 10 ounces, of the 80% salt solution; the other 40 ounces of the 30% salt solution.
CHECK:
.80(10)+.30(40) 8+12 = 20
.40(50) = 20
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 30% salt and Solution B is
80% salt. She wants to obtain 50 ounces of a mixture that is 40% salt. How many ounces of each solution should she use?
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There's no reason to assume that it's NaCl in water.
There are many salts and many solvents.
One or more of them might be able to achieve a concentration of 80%.
If you don't know of a combination that will do this, that is not proof that such a combination does not exist.
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