SOLUTION: 1.Mix a solution that is 30% alcohol with a solution that is 80% alcohol to make 725 mL of a solution that is 60% alcohol. How much (in mL) of each solution should you use? 30

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: 1.Mix a solution that is 30% alcohol with a solution that is 80% alcohol to make 725 mL of a solution that is 60% alcohol. How much (in mL) of each solution should you use? 30      Log On

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Question 1145668:
1.Mix a solution that is 30% alcohol with a solution that is 80% alcohol to make 725 mL of a solution that is 60% alcohol. How much (in mL) of each solution should you use?
30% alcohol solution__ml
80% alcohol solution__ml.
2.A welder has 15 pieces of 4 ft steel angle and 18 pieces of 2 ft steel angle. What is the ratio of pieces of 4 ft steel angle to 2 ft steel angle? (Enter your answer in fraction form.)
Found 3 solutions by solver91311, josgarithmetic, greenestamps:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the amount of 30% solution.



Solve for , then calculate

One problem per post.


John

My calculator said it, I believe it, that settles it

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
(1)

x ml of 80%
725-x ml of 30%
725 ml of 60%

80x%2B30%28725-x%29=60%2A725
-

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


First a standard algebraic solution to the mixture problem....

x = mL of 30% alcohol solution
725-x = mL of 80% alcohol solution

.30(x) = amount of alcohol in x mL of 30% solution
.80(725-x) = amount of alcohol in (725-x mL of 80% solution
.60(725 = amount of alcohol in 725 mL of 60% solution

.30%28x%29%2B.80%28725-x%29+=+.60%28725%29
30%28x%29+%2B+80%28725-x%29+=+60%28725%29
30x+%2B+58000-80x+=+43500
14500+=+50x
x+=+290

ANSWER: 290 mL of the 30% solution and 725-290 = 435 mL of the 80% solution.

That's a perfectly good method for solving mixture problems like this.

But there is a much easier way....

Now a much easier solution, based on where the 60% lies between the 30% and 80%....

(1) 60 is 3/5 of the way from 30 to 80 (look at the 3 numbers 30, 60, and 80 on a number line; 30 to 60 is 30; 30 to 80 is 50; 30/50 = 3/5)
(2) Therefore, 3/5 of the mixture should be the higher percentage solution.

ANSWER: 3/5 of 725 mL, or 435 mL, of 80% alcohol solution; 2/5 of 725 mL, or 290 mL, of 30% alcohol solution