SOLUTION: how many gallons each of 25% alcohol and 35% alcohol should be mixed to get 10 gallons of 32% alcohol?

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Question 328754: how many gallons each of 25% alcohol and 35% alcohol should be mixed to get 10 gallons of 32% alcohol?
Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let A be the amount of 25% alcohol, B 35% alcohol.
1.A%2BB=10
.
.
25A%2B35B=32%2810%29
25A%2B35B=320
2.5A%2B7B=64
Multiply eq. 1 by (-5) and add to eq. 2,
-5A-5B%2B5A%2B7B=-50%2B64
2B=14
B=7
Then from eq. 1,
A%2B7=10
A=3
You need to mix 3 gallons of 25% alcohol and 7 gallons of 35% alcohol.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
how many gallons each of 25% alcohol and 35% alcohol should be mixed to get 10 gallons of 32% alcohol?
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Equation:
alcohol + alcohol = alcohol
0.25 x + 0.35(10-x) = 0.32*10
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Multiply thru by 100 to get:
25x + 35*10 - 35x = 32*10
-10x = -3*10
x = 3 gallons (amt. of 25% alcohol needed in the mixture)
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10-x = 7 gallons (amt. of 35% alcohol needed in the mixture)
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Cheers,
Stan H.
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