Answer: 3000 gallon
Explanation:
Here, The total quantity of 15% alcohol content = 3000 gallon
And, in which quantity of alcohol = 15% of 3000 gallon = 450 gallon.
Let the total quantity of 9% alcohol content = x
In which quantity of alcohol = 9% of x gallon= 9x/100 gallon
Now, according to the question, The wine with a 9% alcohol content will be mixed with 3,000 gallons of wine with a 15% alcohol content in order to achieve the desired 12% alcohol content.
Thus, the total quantity of mixture of 12% alcohol content = The total quantity of 15% alcohol content + total quantity of 9% alcohol content
= 3000 + x
In which quantity of alcohol = 12 % of ( 3000+x) = (360 + 12x/100) gallon ---(1)
But, the quantity of alcohol in 12 % of alcohol content = quantity of alcohol in 15% of alcohol content + quantity of alcohol in 9% of alcohol content
The quantity of alcohol in 12 % of alcohol content = (450 + 9x/100) gallon ---(2)
On equating equation (1) and (2)
We get, 360 + 12x/100 = 450 + 9x/100
⇒ 3x/100 = 90
⇒ x = 3000
Therefore, The total quantity of the mixture of 9% alcohol content = 3000