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

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(52797)   (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 = = 3*5 = 15. Answer. 15 liters of the 35% solution. Answer A).

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    - 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,
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Also, you have this free of charge online textbook in ALGEBRA-I in this site
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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

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Answer by richwmiller(17219)   (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

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