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?

3000 gallon

Step-by-step 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

3000 gallons

Step-by-step explanation:

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step-by-step explanation: