Question 170410
<font size = 7 color = "indigo"><b>Edwin's solution with chart:</font></b>
I get really confused when trying to set these problems up. Can you help me work this one out so I can use it for my other questions please? How many liters of a 40% alcohol solution should be mixed with 40 liters of a 90% solution to get a 50% solution? Thanks for your help.
<pre><font size = 4 color = "indigo"><b>
Make this chart:


               | liters |  %  | pure alcohol
--------------------------------------------
1st solution   |        |     |           
2nd solution   |        |     |            
---------------|--------|-----|-------------
final solution |        |     |          

Let x = liters of 1st solution
and we are given that there are 40 liters
of the 2nd solution, so fill in x and 40 
liters.


               | liters |  %  | pure alcohol
--------------------------------------------
1st solution   |    x   |     |      
2nd solution   |   40   |     |    
---------------|--------|-----|-------------
final solution |        |     |

Add the two to get x+40 liters of final solution.


               | liters |  %  | pure alcohol
--------------------------------------------
1st solution   |    x   |     |      
2nd solution   |   40   |     |   
---------------|--------|-----|-------------
final solution | x+40   |     | 

Put in the three percentages as decimals:


               | liters |  %  | pure alcohol
--------------------------------------------
1st solution   |    x   | .40 |      
2nd solution   |   40   | .90 |     
---------------|--------|-----|-------------
final solution | x+40   | .50 | 

Now get the amount of pure alcohol contained
in each by multiplying by the percentage as
a decimal.


               | liters |  %  | pure alcohol
--------------------------------------------
1st solution   |    x   | .40 |      .40x
2nd solution   |   40   | .90 |   .90(40)  
---------------|--------|-----|-------------
final solution | x+40   | .50 | .50(x+40)

The equation comes from the last column:

.40x + .90(40) = .50(x+40)

Can you solve that for x? If not post again.

answer:  x = 160 liters

Edwin</pre>