SOLUTION: Mr. Ferrer works in the lab at a pharmaceutical company. He needs to make 55 liters of a 27% solution by mixing the 35% solution with the 24% solution. How much of the 35% solution

Algebra ->  Inequalities -> SOLUTION: Mr. Ferrer works in the lab at a pharmaceutical company. He needs to make 55 liters of a 27% solution by mixing the 35% solution with the 24% solution. How much of the 35% solution      Log On


   

Question 1101670: Mr. Ferrer works in the lab at a pharmaceutical company. He needs to make 55 liters of a 27% solution by mixing the 35% solution with the 24% solution. How much of the 35% solution will Mr. Ferrer need to use?
A. 15 L
B. 19 L
C. 55 L
D. 40 L
Found 2 solutions by ikleyn, richwmiller:
Answer by ikleyn(52795) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the volume of the 35% solution, in liters.

Then the volume of the 24% solution is (55-x).


The balance equation is

0.35*x + 0.24(55-x) = 0.27*55  ====>

0.35x + 0.24*55 - 0.24x = 0.27*55  ====>  0.11x = 0.27*55 - 0.24*55 = 0.03*55  ====>  x = %280.03%2A55%29%2F0.11 = 3*5 = 15.


Answer.  15 liters of the 35% solution.  Answer A).

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
in this site.

You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at the 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.



Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Let A denote the 35% solution and B denote the 24% solution which we have.
Let C denote the 27% solution which we want.
Using the method of alligation.
35         3 3/11*55=15 L of 35% solution
      27
24         8 8/11*55=40 L of 24% solution
           11

8= 35 - 27
3= 27 - 24
E.g. There are 3 parts of A plus 8 parts of B
Then 3+8=11 parts total
3/11=0.27272727
0.27272727*55=15
15 L of 35% solution.
55 L-15 L=40 L
40 L of 24% solution.
or
8/11=0.72727273
0.72727273*55=40 L
40 L of 24% solution.
check
0.24 * 40 + 0.35 * 15 = 0.27*55
9.6 + 5.25 = 14.85
14.85 = 14.85
ok