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
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.
