Question 1144999: System of equation problem
Solve using Substitution or Addition
A 12-L cooling system is filled with 25% antifreeze. How many liters must be replaced with 100%
antifreeze to raise the strength to 45% antifreeze? Round your answer to the correct number of
significant figures.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39631)   (Show Source):
Answer by ikleyn(52925)  (Show Source):
You can put this solution on YOUR website! .
In my view, there is some misunderstanding with this problem, how it is presented/worded in this post.
This problem is for one unknown variable, which is the volume under the question.
Accordingly, the standard and traditional way to solve it is using one single equation.
NO system of equations is needed, and NO Substitution or Elimination methods are used.
Below is this traditional solution method.
Let V be the volume to drain off from 12 liters of the 25%-antifreeze.
Step 1: Draining. After draining, you have 12-V liters of the 25% antifreeze.
It contains 0.25*(12-V) of pure antifreeze.
Step 2: Replacing. Then you add V liters of the pure antifreeze (the replacing step).
After the replacing, you have the same total liquid volume of 12 liters.
It contains (0.25(12-V) + V) liters of pure antifreeze.
So, the antifreeze concentration after replacement is  .
It is the ratio of the pure antifreeze volume to the total volume.
Therefore, your "concentration equation" is
= 0.45. (1)
The setup is done and completed.
To solve the equation (1), multiply both sides by 12. You will get
0.25*(12-V) + V= 0.45*12,
3 - 0.25V + V= 5.4,
0.75V = 5.4 - 3 = 2.4 ====> V =  = 3.2 liters.
Answer. 3.2 liters of the 25% antifreeze must be drained and replaced by 3.2 liters of pure antifreeze.
Check.  = 0.45. ! PRECISELY Correct !
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In this site, there is entire bunch of introductory 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 alloys
- Typical word problems on mixtures from the archive
Read them and become an expert in solution mixture word problems.
Notice that among these lessons there is one on antifreeze solutions marked by (*).
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 textbook in the section "Word problems" 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.
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