Q:

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?

Accepted Solution

A:
Answer: 3000 gallonStep-by-step explanation:Here, The total quantity of 15% alcohol content = 3000 gallonAnd, in which quantity of alcohol = 15% of 3000 gallon = 450 gallon.Let the total quantity of 9% alcohol content  = xIn which quantity of alcohol = 9% of x gallon= 9x/100 gallonNow, 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 + xIn 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 = 3000Therefore, The total quantity of the mixture of 9% alcohol content = 3000