SOLUTION: A chemist wants to make 57 ml of a 17% acid solution by mixing an 11% acid solution and a 20% acid solution. How many milliliters of each solution should the chemist use?
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Question 1148679: A chemist wants to make 57 ml of a 17% acid solution by mixing an 11% acid solution and a 20% acid solution. How many milliliters of each solution should the chemist use? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52781) (Show Source):
Let x be the volume of the 20% solution, in milliliters; then the volume of the 11% solution is (57-x) mL.
Your basic equation is
= 0.17*57
saying that the total pure acid volume in the ingredients is equal to the pure acid volume in the mixture.
From the equations, express x and calculate
x = = 38.
ANSWER. 38 mL of the 20% solution and the rest, 57-38 = 19 mL of the 11% solution.
CHECK. I will check if the concentration is correct.
Concentration = = 0.17. ! Precisely correct !
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Here is a quick alternative to the standard algebraic solution method shown by the other tutor (assuming, of course, that an algebraic solution method is not required....)
(1) 17% is 2/3 of the way from 11% to 20%. (Picture the three percentages on a number line -- 11, 17, and 20. 11 to 20 is 9; 11 to 17 is 6; 6 is 2/3 of 9.)
(2) That means 2/3 of the mixture must be the higher percentage ingredient.
ANSWER: 2/3 of 57ml, or 38ml, of the 20% acid solution; the other 19ml of the 11% acid solution.
