SOLUTION: Theresa Morgan, a chemist, has a 25% hydrochloric acid solution and a 55% hydrochloric acid solution. How many liters of each should she mix to get 465 liters of a hydrochloric aci

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Question 1129724: Theresa Morgan, a chemist, has a 25% hydrochloric acid solution and a 55% hydrochloric acid solution. How many liters of each should she mix to get 465 liters of a hydrochloric acid solution with a 45% acid concentration?
___ liters of 25% H
____ liters of 55% H

Found 3 solutions by josgarithmetic, Boreal, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
h, amount of the 55% acid to use
465-h, amount of the 25% acid to use
55h%2B25%28465-h%29=45%2A465
-
55h-25h%2B25%2A465=45%2A465
30h%2B25%2A465=45%2A465
30h=%2845-25%29465
30h=20%2A465
h=%282%2F3%29465
highlight%28h=310%29--------liters of the 55% HCl



----------------MIS-HANDLED METHOD--------------------
From 25% up to 55%
Want 45% result
25, 30, 35, 40, 45, 50, 55--------
%2845-25%29%2F%2855-25%29
2%2F3
45 % is 2%2F3 of the way from 25% to 55%.

Liters of the 25% HCl?
cross%28465%282%2F3%29%29

cross%28310%2ALiters%29-----of the 25% HCl

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
One way is to note that 45% is 2/3 of the way between 25% and 55%, so twice as much of the 55% will be used.
Or,
x at 25%
465-x at 55%
.25x+.55(465-x)=465*.45=209.25
.25x+255.75-.55x=209.25
-.30x=-46.50
x=155 liters
465-x=310 liters, twice as much.

Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.

The solution by @Boreal is correct.

The solution by @josgarithmetic is   T O T A L L Y   W R O N G.


@josgarithmetic is trying to follow recommendations by the tutor @greenestamps in this forum,  but having no understanding
on how to do it in a right way - he does it in a wrong way.

For your safety, simply ignore the solution and the answer by @josgarithmetic !.


The correct answer is  155 liters of the  25% solution and  310 liters of the  55% solution.


Check.    0.25*155 + 0.55*310 = 209.25 = 0.45*0.465.         ! Correct !