Question 1105681: The Patronete Winery's tastiest wine must have a 12% alcohol content. How many gallons of wine with a 9% alcohol content must be mixed with 3,000 gallons of wine with a 15% alcohol content in order to achieve the desired 12% alcohol content?
Found 4 solutions by ankor@dixie-net.com, Alan3354, josgarithmetic, greenestamps:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The Patronete Winery's tastiest wine must have a 12% alcohol content.
How many gallons of wine with a 9% alcohol content must be mixed with 3,000 gallons of wine with a 15% alcohol content in order to achieve the desired 12% alcohol content?
:
let x = amt of 9% wine required
An equation using the decimal equiv of per cent
.09x + .15(3000) = .12(x+3000)
.09x + 450 = .12x + 360
450 - 360 = .12x - .09x
90 = .03x
x = 90/.03
x = 3000 gal of 9% required
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! The Patronete Winery's tastiest wine must have a 12% alcohol content. How many gallons of wine with a 9% alcohol content must be mixed with 3,000 gallons of wine with a 15% alcohol content in order to achieve the desired 12% alcohol content?
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12 is the average of 9 & 15
--> equal amounts
Answer by josgarithmetic(39620)  (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
You have 3 answers to your question so far. Let me comment....
The first tutor ankor... gave a perfectly good algebraic solution, using the standard method.
The third tutor Josgarithmetic solved the wrong problem, making a total of 3000 gallons of the 12% wine instead of using 3000 gallons of the 15% wine.
The second tutor alan3354 encouraged you to use your common sense instead of blindly plunging into a formal mathematical solution. Doesn't it make sense that, since the 12% you want is halfway between the 15% and the 9%, you need to use equal amounts?
The methods of algebra are useful; you should learn them. But don't forget that you can often solve problems by using your BRAIN to think logically.
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