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a lab tech needs to make a 60-liter batch of a 40% acid solution, how can the lab tech combine a batch of an acid solution that is pure acid with another that is 20% to get desired concentration
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Let x = the volume of the pure acid (in liters),
and y = the volume of the 20% acid solution to combine with.
Then you have two equations
x + y = 60, (1) (for the total combined volume)
x + 0.2y = 0.4*60. (2) (for the acide amount)
Rewrite the system by simplifying (2):
x + y = 60, (1')
x + 0.2y = 24. (2')
From (1'), express x = 60-y and substitute it into (2'). You will get a single equation for the unknown y:
(60-y) + 0.2y = 24.
Simplify and solve it:
60 - y + 0.2y = 24,
60 - 0.8y = 24,
60 - 24 = 0.8y,
36 = 0.8y,
y = = 45 liters of the 40% acid solution.
Now, x = 60 - 45 = 15 liters of pure acid.