SOLUTION: I've been on this problem for a very long time. I've been trying to translate the problem into a system for elimination but I just can't seem to do it correctly. A chemist needs

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Question 1052087: I've been on this problem for a very long time. I've been trying to translate the problem into a system for elimination but I just can't seem to do it correctly.
A chemist needs 5 liters of a 29% acid solution. He has a 25% solution and a 50% solution available to form the mixture. How much of each should be used to form the 29% solution?
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
You might try substitution method instead, if you believe the coefficients make the work too messy for Elimination.

u, how much liters of the 25% acid
v, how much liters of the 50% acid


Five liters wanted.


Fifty percent acid solution wanted.



CAN YOU SIMPLIFY AND ADJUST THE FORM OF THE CONCENTRATION EQUATION?






WHAT IS THE SIMPLIFIED SYSTEM OF EQUATIONS?


You really will have no trouble using Elimination Method for this system.
Multiply the volume-sum equation by 5.
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
I've been on this problem for a very long time. I've been trying to translate the problem into a system for elimination
but I just can't seem to do it correctly.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There is entire bunch of the 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
in this site.

Read them and become an expert in solution the 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".

The textbook contains many other solved word problems, as well as many other interesting and useful things.


Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
I've been on this problem for a very long time. I've been trying to translate the problem into a system for elimination but I just can't seem to do it correctly.
A chemist needs 5 liters of a 29% acid solution. He has a 25% solution and a 50% solution available to form the mixture. How much of each should be used to form the 29% solution?
Let amount of 25% solution to mix, be T, and amount of 50%, F

Then, T + F = 5 ----- eq (i)

Also, .25T + .5F = .29(5)____.25T + .5F = 1.45 ------- eq (ii)

- .5T - F = - 2.9 ------ Multiplying eq (ii) by - 2 ------- eq (iii)

Now, just add eqs (iii) & (i) to ELIMINATE F and determine T, the amount of 25% solution to mix.

Substitute the value of T into any of the 1st 2 ORIGINAL equations to determine the value of F, the amount of 50% solution. 

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