.
Let W be the volume to drain off from 80 liters of solution.
Step 1: Draining. After draining, you have (80-W) liters of the 30% acid solution.
Step 2: Replacing. Then you add W liters of the 70% solution (the replacing step).
After the replacing, you have the same total liquid volume of 80 liters.
It contains 0.3*(80-W) + 0.7*W of pure solvent.
So, your "concentration equation" is
= 0.4. (1)
At this point, the setup is done and completed.
Now you need to solve your basic equation (1).
As the first step, multiply both sides by 80, and then simplify
0.30*(80-W) + 0.7*W = 0.4*80
24 - 0.3W + 0.7W = 32
0.4W = 32 - 24 = 8
W = = 20.
ANSWER. 20 liters of the original 30% solution should be drained and replaced by 20 liters of the 70% solutions.
CHECK. = 0.4. ! Precisely correct !
Solved.
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There is entire bunch of lessons covering various types of mixture problems
- Mixture problems
- More Mixture problems
- Solving typical word problems on mixtures for solutions
- Word problems on mixtures for antifreeze solutions (*)
- Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts
- Word problems on mixtures for dry substances like candies, dried fruits
- Word problems on mixtures for dry substances like soil and sand
- Word problems on mixtures for alloys
- Typical word problems on mixtures from the archive
- Advanced mixture problems
- Advanced mixture problem for three alloys
- OVERVIEW of lessons on word problems for mixtures
in this site.
A convenient place to quickly observe these lessons from a "bird flight height" (a top view) is the last lesson in the list.
Read them and become an expert in solution the mixture word problems.
Specially for "draining - replacing" mixture problems see the lesson marked (*) in the list.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Mixture problems".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.