Question 403138
based on the problem statement, we can create a mathematical model that says

x + y = 42 liters

where 
x = number of liters of the 67% strength solution
y = number of liters of the 46% strength solution


also based on the problem statement, we can create another mathematical model that says

0.67x + 0.46y = 0.55(42) = 23.1 liters  (note: that is the amount of 'pure' 100% acid) 

now we have two separate independent equations and two unknowns

we can substitute and solve

y = (42 - x) so

0.67x + 0.46(42 - x) = 23.1


0.67x - 0.46x + 19.32 = 23.1

0.21x + 19.32 = 23.1

0.21x = 3.78

x = 3.78/0.21

x = 18 liters of the 67% strength solution
y = 24 liters of the 46% strength solution