SOLUTION: How much of a 40% solution of alcohol and how much of a 80% solution should be mixed to give 40 gallons of a 50% solutions?
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Question 1144648: How much of a 40% solution of alcohol and how much of a 80% solution should be mixed to give 40 gallons of a 50% solutions?
Found 3 solutions by josmiceli, josgarithmetic, ikleyn:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = gallons of 40% solution needed
Let = gallons of 80% solution needed
---------------------------------------------------
(1)
(2)
------------------------------------
(1)
(1)
(1) subtract (2) from (1)
(2)
---------------------------
and
(2)
(2)
---------------------------
30 gallons of 40% solution and 10 gallons of
80% solution are needed
----------------------------
check:
(1)
(1)
(1)
(1)
(1)
OK
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
How much of a 40% solution of alcohol and how much of a 80% solution should be mixed to give 40 gallons of a 50% solutions?
---------------------------------------------------------------------------
How much of a L% solution of alcohol and how much of a 2L% solution should be mixed to give M gallons of a T% solutions?
------------------------------------------------------------------------
x of the L% solution
M-x of the 2L% solution
Solve for x.
-------------substitute your values and evaluate.
Answer by ikleyn(52793) (Show Source): You can put this solution on YOUR website!
.
If you are a beginner in solving such problems (word mixture problems), then ignore the post by @josgarithmetic.
If you are a school Math teacher, teaching school Math students, who are beginners in solving such problems,
then the same recommendation works : ignore the post by @josgarithmetic.
If you are just advanced person in solving such problems and in Algebra, in general, then you may use his post.
But I can hardly imagine a person, who just knows this subject and comes to this forum for help.
So, I firmly believe that the set of visitors of this forum, to whom his writing might be useful, is EMPTY.
Follow the solution by the tutor @josmiceli.
It is totally adequate for beginners.
---------------
It is a standard and typical mixture problem.
In this site, there is a huge collection of lessons covering various types of mixture word problems.
Start from these introductory lessons
- Mixture problems
- More Mixture problems
- Solving typical word problems on mixtures for solutions
- Typical word problems on mixtures from the archive
You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization, from very detailed to very short.
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.
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