SOLUTION: You need 1190 mL of a 70% alcohol solution. On hand, you have a 85% alcohol mixture. How much of the 85% alcohol mixture and pure water will you need to obtain the desired solution

Question 1098348: You need 1190 mL of a 70% alcohol solution. On hand, you have a 85% alcohol mixture. How much of the 85% alcohol mixture and pure water will you need to obtain the desired solution?

Found 3 solutions by josgarithmetic, richwmiller, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

Solve for x.
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
Let A denote the 85% solution and B denote the 0% solution which we have.
Let C denote the 70% solution which we want.
Using the method of alligation.
70= 70 - 0
15= 85 - 70
E.g. There are 70 parts of A plus 15 parts of B
Then 70+15=85
0.82352941*1190=980
980 mL of 85% solution.
1190-980=210
210 mL of 0% solution.(pure water)
check
0 * 210 + 0.85 * 980 = 0.7*1190
0 + 833.0 = 833.0
833.0 = 833.0
ok
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

Let x be the volume of the 85% alcohol mixture to obtain the desired 1190 mL of the 70% solution. Then the volume of water is (1190-x) mL, to provide the total volume of the final mixture of 1190 mL. "x" mL of the 85% alcohol mixture contains 0.85*x mL of the pure alcohol. Exactly this amount of the pure alcohol goes to the final solution. Thus the final solution contains 0.85*x mL of the pure alcohol and has the volume of 1190 mL. The fraction is the ratio of the pure alcohol volume to the total liquid volume, i.e concentration. According to the condition, the concentration of the final mixture must be 70%, i.e. 0.7. It gives you an equation = 0.7. From the equation, x = = 980. Answer. 980 mL of the 85% solution should be mixed with 1190-980 = 210 mL of water to get 1190 mL of the 70% solution. Check. = 0.7, or 70%. ! Correct !

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