# Having trouble with Linear Equations and Inequalities.

#### Envyy

Hey everyone. I am having trouble with this problem and other similar problems:

"In the lab, Bill has two solutions that contain alcohol and is mixing them with each other. He uses 100 mL less of solution A than solution B. Solution A is 17% alcohol and Solution B is 20% alcohol. How many mL of Solution A does he use, if the resulting mixture has 94 mL of pure alcohol?"

Could anyone help me with this? I only need to get 3 more of these problems right and then I'll be done. But I am really stuck.

#### HallsofIvy

MHF Helper
Let A be the amount of solution "A" you use and B the amount of solution "B", both in ml. "He uses 100 mL less of solution A than solution B" so A= B- 100. The amount of alcohol from solution "A" is 0.17A and the amount of alcohol from solution "B" is 0.20B. You want the final solution to include 94 ml of alcohol so 0.17A+ 0.20B= 94.

Solve A= B- 100 and 0.17A+ 0.20B= 94 for A and B.

#### DenisB

Example:
a=300: 300 * .17 = 51
b=400: 400 * .20 = 80
That's 51+80 = 131 ml of pure alcohol .

In case you're thinking of ending up with a percentage.