Solution concentration calculation

If we mix 4 l and 6 l of differently concentrated salt solutions, we get a 12% solution. If we use 6 l of the first and 4 l of the second solution, we get a 13% solution. What is the concentration of each solution?

Final Answer:

a =  15 %
b =  10 %

Step-by-step explanation:


4a + 6b = 12·(4+6)
6a+4b = 13·(6+4)

4·a + 6·b = 12·(4+6)
6·a+4·b = 13·(6+4)

4a+6b = 120
6a+4b = 130

Pivot: Row 1 ↔ Row 2
6a+4b = 130
4a+6b = 120

Row 2 - 4/6 · Row 1 → Row 2
6a+4b = 130
3.33b = 33.33


b = 33.33333333/3.33333333 = 10
a = 130-4b/6 = 130-4 · 10/6 = 15

a = 15
b = 10

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You need to know the following knowledge to solve this word math problem:

algebrabasic operations and conceptsUnits of physical quantitiesthemes, topicsGrade of the word problem

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