SOLUTION: Two alcohol solutions consists of a 35 gallons of 35% alcohol and other solutions containing 50% alcohol. If the two solutions are combined together, they will have a mixture of 40

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Question 1197844: Two alcohol solutions consists of a 35 gallons of 35% alcohol and other solutions containing 50% alcohol. If the two solutions are combined together, they will have a mixture of 40% alcohol. How many gallons of the solutions containing 50% alcohol?
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Two alcohol solutions consists of a 35 gallons of 35% alcohol and other solutions containing 50% alcohol. If the two solutions are combined together, they will have a mixture of 40% alcohol. How many gallons of the solutions containing 50% alcohol?
                 gals. of| % of  |  gals. of    |
                  liquid |alcohol|pure alcohol  |
First solution  |  35    |  0.35 | 0.35(35)     |  <--this
Second solution |   x    |  0.50 | 0.50x        |  <--plus this         
Final solution  | 35+x   |  0.40 | 0.40(35+x)   |  <--equals this

0.35(35)+0.50x = 0.40(35+x)
   12.25+0.50x =  14+0.40x

You finish solving for x

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


Here are two variations of a method that can be used to solve any 2-part "mixture" problem like this without formal algebra.

(1) The 40% of the mixture is 5% away from the 35% of one ingredient and 10% away from the 50% of the other ingredient. So 40% is "twice as close" to 35% as it is to 50%. That means the amount of the 35% solution must be twice the amount of the 50% solution. Since there are 35 gallons of the 35% solution, there must be 35/2 = 17.5 gallons of the 50% solution.

ANSWER: 17.5 gallons of the 50% alcohol

(2) Look at the three percentages on a number line -- 35, 40, and 50 -- and observe/calculate that 40 is one-third of the way from 35 to 50. That means 1/3 of the mixture is the ingredient with the higher percentage. So the 35 gallons of 35% alcohol is 2/3 of the total; that means the 1/3 of the total that is the 50% alcohol is half of 35 gallons, which is 17.5 gallons.

ANSWER: 17.5 gallons of the 50% alcohol

CHECK:
.35(35)+.50(17.5) = 12.25+8.75 = 21
.40(35+17.5) = .40(52.5) = 21
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