Alcohol mixing

How much 55% alcohol must we pour into 1500 g 80% alcohol to form a 60% alcohol? How much is 60% alcohol created?

Correct answer:

x =  6000 g
y =  7500 g

Step-by-step explanation:

m2​=1500 g  0.55⋅ x+0.80⋅ m2​=0.60⋅ y x+m2​=y 0.55⋅ x+0.80⋅ 1500=0.60⋅ y x+1500=y  0.55x−0.6y=−1200 x−y=−1500  Pivot:Row1↔Row2 x−y=−1500 0.55x−0.6y=−1200  Row2−0.54999999999995⋅ Row1→Row2 x−y=−1500 −0.05y=−375  y=−0.05−375​=7500.00000001 x=−1500+y=−1500+7500.00000001=6000.00000001=6000 g  x=6000 y=7500

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