Question

The Davidson Winery is noted for its Regal Champagne. It takes the blending of 1,000 bushels of a mixture of two varieties of grapes to achieve the Regal specification of 12% alcohol content for its champagne. One of the two varieties of grape contains a 10% alcohol content and the other contains a 15% alcohol content. How many bushels of each variety are needed?

Answer 1

Answer: 600 bushels of 10% alcohol content and 400 bushels of 15% alcohol content.

Step-by-step explanation:

Let we add x quantity of 10% of alcohol content and y quantity of 15% alcohol content for making 12% of alcohol content mixture.

Then according to the question, 10% of x + 15 % of y = 12% of 1000

⇒ 0.1x + 0.15y = 120

⇒ 10x + 15y = 1200

⇒ 2x +3y  = 2400 -------- (1)

And, x + y = 1000

⇒ 2x + 2y = 2000 ---------(2)

Equation 1) - equation 2)

We get y = 400

By putting the value of y in equation 1),

⇒2x + 1200 = 2400

⇒ 2x = 1200

⇒ x = 600

Thus, he needs to mix 600 bushel of 10% of alcohol content with 400 bushels of 12% of alcohol content for getting 1000 bushels of 12% of alcohol content.