There are two mixtures. One mixture contains 5% alchol and the other mixture contains 12% alchol. How much of each should be mixed to make 1000 gallons with 10% alchol
Accepted Solution
A:
Answer:to make 1000 gallons with 10% alcohol, we need 714.3 gallons of mixture that contains 5% alcohol and 285,7 gallons of mixture that contains 12% alcohol. Step-by-step explanation:According to the statement, there are two mixtures. One mixture contains 5% alcohol and the other contains 12% alcohol. We want to make 1000 gallons with 10% alcohol, so we have the following system of equations:A + B = 1000 gallons. [1]0.05A + 0.12B = 0.1(1000) ⇒ 0.05A + 0.12B = 100 [2](Where 'A' represents the mixture that contains 5% alcohol and 'B' the one that contains 12% alcohol).Solving the system of equations:A + B = 1000 ⇒ A = 1000 - B [3][3] → [2]0.05(1000 - B) + 0.12B = 100 ⇒ 50 - 0.05B + 0.12B = 100 ⇒ 0.07B = 50 ⇒ B = 714.28 ≈ B=714.3 [4][4] → [1]A + B = 1000 ⇒ A + 714.3 = 1000 ⇒ A = 285,7Therefore, to make 1000 gallons with 10% alcohol, we need 714.3 gallons of mixture 'A' and 285,7 gallons of mixture 'B'