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 = 285,7
Therefore, to make 1000 gallons with 10% alcohol, we need 714.3 gallons of mixture 'A' and 285,7 gallons of mixture 'B'
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