SOLUTION: how much of a 25% acid solution should be mixed with 5 L of a 15% acid solution to obtain a 20% acid solution?

Algebra.Com
Question 697704: how much of a 25% acid solution should be mixed with 5 L of a 15% acid solution to obtain a 20% acid solution?
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
how much of a 25% acid solution should be mixed with 5 L of a 15% acid solution to obtain a 20% acid solution?
---------------
20 is the average of 15 & 25, so it's equal amounts.
5 liters.

Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
The other tutor's answer is correct, but his method will work ONLY
when the percentage desired is exactly half-way between the two
percentages.  Here is a more general way to do the problem, which will
work in ALL mixture problems: 

Make this chart:

              amt of liquid     % acid   amt of pure acid contained 
1st solution       
2nd solution        
final solution

Let x be the answer, so fill that in first     




              amt of liquid     % acid   amt of pure acid contained 
1st solution        x           
2nd solution      
final solution     

We are told that there are 5 L of the second solution, so

              amt of liquid     % acid   amt of pure acid contained 
1st solution        x           
2nd solution        5             
final solution     

Now we add x PLUS 5 to get the amt of final liquid, so we fill
x+5 in

              amt of liquid     % acid   amt of pure acid contained 
1st solution        x           
2nd solution        5         
final solution     x+5          

Next we fill in the three percentages as decimals:

              amt of liquid     % acid   amt of pure acid contained 
1st solution        x             .25           
2nd solution        5             .15            
final solution     x+5            .20          

Then we multiply the three amts of liquid by the percentages expressed
as decimals to get the amt of pure acid in each amount:

              amt of liquid     % acid   amt of pure acid contained 
1st solution        x             .25            .23x
2nd solution        5             .15            .15(5)
final solution     x+5            .20            .20(x+5)

The equation comes from:

                 


                 .25x + .15(5) = .20(x+5)

Multiply through by 100  

                   25x + 15(5) = 20(x+5)
                      25x + 75 = 20x + 100
                            5x = 25
                             x = 5              
Edwin

RELATED QUESTIONS

How much of a 25% acid solution should be mixed with 5L of a 15% acid solution to obtain... (answered by Alan3354)
Can you explain how to solve this word problem?: How much of a 25% acid solution should... (answered by mananth)
How much 10% acid solution should be mixed with 1 L of 25% acid solution to produce a... (answered by ikleyn,Alan3354)
How many liters of a 15% acid solution should be mixed with 30 liters of a 40% acid... (answered by lostin)
how much of a 25% acid solution should be mixed with a 50% acid solution to obtain 500... (answered by Abbey)
How many gallons of 5% acid solution should be mixed with 20 gallons of a 10% acid... (answered by stanbon)
How many gallons of 5% acid solution should be mixed with 20 gallons of a 10% acid... (answered by lwsshak3)
how much pure acid should be mixed with 3 gallons of 20% acid solution to get a 40% acid... (answered by tommyt3rd)
15 ml of 25% acid solution must be mixed with how much 30% acid to yield a 27% acid... (answered by stanbon)