Algebraic mixture problem... Need help?

Question

I am getting so frusterated with not understading this problem. I need to put it into a table to solve. Help?

A chemist has 2 solutions. Solution A is 8% acetic acid, and solution B is 20% acetic acid. If he wants 4 liters of 11% acetic acid , how much of solutions A and B should he combine?

Answer 1

I see a few people have told you the answer but you need to know how to do it.
For mixture problems you need two equations. one relating the quantities of the ingredients and one relating the strengths. Then you solve a system of these two to find the amounts of the ingredients.
Here, let's call W = the amount of 8% (weak) solution and S = the amount of 20% (strong) solution.
(I always recommend using letters that stand for what you're working with rather than arbitrary letters such as x and y or A and B, this helps you to make sense of the process and the answer)
Since you want a total of 4 liters, your equation relating the quantities of your ingredients is
S + W = 4
The equation relating the strengths of the ingredients is a little trickier but it always follows the same format. Here you're comparing the actual amount of acetic acid in the solution. So this equation is
(.20)S + (.08) W = (.11)4
If you like you can multiply this equation by 100 to get rid of the decimals...
20S + 8W = 44
Now your system is
..S + ..W = 4
20S + 8W = 44
Solve this system by any method you prefer...
I'll use linear combination, and multiply the top equation by -8 to get rid of the W
-8S + -8W = -32
20S + 8W = 44
----------------------
12S = 12
S = 1
Since S + W = 4, W = 3
Check:
(.2)(1) + (.08)(3) = 4x(.11) = .44
So you need 1 liter of strong (20%) solution and 3 liters of weak (8%) solution
For more info put "tutorial mixture problems" into your search window and find one that helps you. Here's a good one...
http://math.uww.edu/~mcfarlat/141/ Gp to "story problems" and then scroll thru the menu choices to "mixture problems". Other good tutorials on this site as well.

Answer 2

you need 3 of a and 1 of b

Answer 3

20% + 8% + 11% divide by 3