<PRE><B>Question 1118558</B>
&lt;br&gt;
Yes; in the real world the problem as stated can&#39;t happen, because the salt percentages are not possible.&lt;br&gt;
However, you are not responsible for the fact that the problem that was given to you can&#39;t happen; the reason you asked the question was to get help learning how to solve the problem.&lt;br&gt;
Algebraically, the traditional approach is something like this....&lt;br&gt;
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.&lt;br&gt;
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:&lt;br&gt;
{{{.70(x) + .95(50-x) = .90(50)}}}&lt;br&gt;
That equation can be solved with basic algebra; I leave it to you.&lt;br&gt;
But there is a much easier way to solve this kind of problem, if an algebraic solution is not required.&lt;br&gt;
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.&lt;br&gt;
The fastest way to explain how to solve your problem is this:&lt;br&gt;
&quot;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.&quot;&lt;br&gt;
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.&lt;br&gt;
Let&#39;s take a closer look at this method.&lt;br&gt;
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%.&lt;br&gt;
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.</PRE>