Question 1118558: A scientist has two solutions which she has labeled solution Aand solution B. Each contain salt. She knows that solution A is 70% salt and solution B is 95% salt. She wants to obtain 50 ounces of a mixture that is 90% salt. How many ounces of each solution should she use ?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! Salt solution in water is NEVER 70%, or 95%, or 90%. Normally at "room" temperature, saturated salt in water solution is about 24 or 25%. Even at elevated temperature of the solvent water, NOTHING over 40%.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Yes; in the real world the problem as stated can't happen, because the salt percentages are not possible.
However, you are not responsible for the fact that the problem that was given to you can't happen; the reason you asked the question was to get help learning how to solve the problem.
Algebraically, the traditional approach is something like this....
let x be the number of ounces of 70% solution; then (50-x) is the number of ounces of 95% solution. You want x ounces of 70% solution combined with (50-x) ounces of 95% solution to give you 50 ounces of 90% solution.
So write an equation saying that the total amount of salt in the two ingredients is equal to the amount of salt in the final mixture:
That equation can be solved with basic algebra; I leave it to you.
But there is a much easier way to solve this kind of problem, if an algebraic solution is not required.
The ratio in which the two ingredients have to be mixed is directly related to where the percentage of the mixture lies between the percentages of the two ingredients.
The fastest way to explain how to solve your problem is this:
"The 90% target solution is 4/5 of the way from 70% to 95%; that means 4/5 of the mixture must be the 95% ingredient."
Since 4/5 of 50 ounces is 40 ounces, that makes the answer 40 ounces of the 95% solution and 10 ounces of the 70% solution.
Let's take a closer look at this method.
Imagine you are starting with the 70% solution and adding the 95% solution. The more of the 95% solution you add, the closer the percentage of the mixture comes to 95%. If you add an equal amount of the 95% solution (so that 1/2 of the mixture is the 95% solution) then the percentage of the mixture will be halfway between 70% and 95%. If you add 4 times as much of the 95% solution as you have 70% solution, then 4/5 of the mixture will be the 95% solution, and the percentage of the mixture will be 4/5 of the way from 70% to 95%.
So, looking at the required calculations with the given percentages for your problem again, we see that from 70 to 95 is 25, and from 70 to 90 is 20; that means the fraction of the mixture that must be the 95% solution is 20/25 = 4/5.
|
|
|
