.
From the condition, you have THESE two equations
x + y + 1 = 30, (1) (total volume)
0.1x + 0.2y = 0.15*30. (2) (soap contents)
Simplify both equations:
x + y = 29, (3)
1x + 2y = 45. (4)
Now subtract eq(3) from eq(4). You will get
y = 45 - 29 = 16 .
Then from eq(1), x = 29-16 = 13.
Answer. 13 quart of the 10% soap solution plus 16 quart of the 20% soap solution plus one quart of pure water.
Check. 0.1*13 + 0.2*16 = 4.5;
0.15*3 = 4.5. ! Correct !
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If you want to learn on how to solve mixture problems, specially for you there are the lessons in this site,
covering basic mixture problems, with detailed algebraic solutions:
- 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
in this site.
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Read them and become an expert in solution mixture word problems.
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.