Question 1123595
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Here is an alternative to the traditional algebraic solution method shown by the other tutor for solving problems like this where two ingredients are being mixed.<br>
If you understand how to use this method, it will get you to the solution to problems like this with far less work than the algebraic method.<br>
(1) You are starting with a 10% solution and adding 5% solution; you want to end up with a mixture of 8%.  As you begin adding 5% solution, the percentage of the mixture decreases from 10% towards 5%.<br>
(2) Here is the key to this method: 8% is 2/5 of the way from 10% to 5%; that means 2/5 of the mixture must be the added 5% solution.<br>
(3) 2/5 being the 5% solution means 3/5 is the 10% solution you started with.<br>
(4) 2/5 and 3/5 means the ratio of the amounts of the two ingredients is 2/5:3/5, or 2:3.  In other words, you need 2 parts of the added 5% salt solution to 3 parts of the original 10% salt solution.<br>
(5) Since you started with 15 liters of the 10% salt solution, the 2:3 ratio means you need 10 liters of the 5% salt solution.<br>
Answer: 10 liters of the 5% salt solution.