Alcohol mixture

We have to produce 0.2 kg of 60% alcohol from 55% and 80% alcohol. How many of them do we use in the solution?

Correct answer:

a =  0.16
b =  0.04

Step-by-step explanation:


0.55a +0.80b = 0.60·0.20
a+b=0.2

0.55·a +0.80·b = 0.60·0.20
a+b=0.2

0.55a+0.8b = 0.12
a+b = 0.2

Pivot: Row 1 ↔ Row 2
a+b = 0.2
0.55a+0.8b = 0.12

Row 2 - 0.55 · Row 1 → Row 2
a+b = 0.2
0.25b = 0.01


b = 0.01/0.25 = 0.04
a = 0.2-b = 0.2-0.04 = 0.16

a = 4/25 = 0.16
b = 1/25 = 0.04

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