SOLUTION: What volume of each of a 5% acid solution and a 70% acid solution should be combined to form 44 mL of a 50% solution? Set up the appropriate euations and solve the system using the

Question 233628: What volume of each of a 5% acid solution and a 70% acid solution should be combined to form 44 mL of a 50% solution? Set up the appropriate euations and solve the system using the inverse of the coefficient matrix.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let x = the number of ml. of the 5% acid solution, then (44-x) would equal the number of ml. of the 70% acid solution.
Write the equation in terms of the amount of acid in each of these after changing the percentages to their decimal equivalents.
x*(0.05)+(44-x)(0.7) = 44(0.5) Simplify and solve for x.
0.05x+30.8-0.7x = 22 Combine like-terms.
-0.65x+30.8 = 22 Subtract 30.8 from both sides.
-0.65x = -8.8 Divide both sides by -0.65
x = 13.54 rounded to nearest hundredth.
You would need 13.54ml of the 5% acid solution and 30.46ml of the 70% acid solution to obtain 44ml of 50% acid solution.
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