In the lab, Mary has two solutions that contain alcohol and is mixing them with each other. She uses 500 milliliters less of Solution A than Solution B. Solution A is 10% alcohol and Solution B is 15% alcohol. How many milliliters of Solution B does she use, if the resulting mixture has 125 milliliters of pure alcohol?
add up the amount of alcohol in each part, and the result
0.10(b-500) + 0.15b = 1.00 * 125
To find the amount of Solution B that Mary uses, we need to set up an equation based on the information given.
Let's assume Mary uses x milliliters of Solution B.
Since Solution A is 500 milliliters less than Solution B, the amount of Solution A used will be (x - 500) milliliters.
Now, let's calculate the amount of alcohol in each solution used:
- The concentration of alcohol in Solution A is 10%, so the amount of alcohol in Solution A used will be (10/100)(x - 500).
- The concentration of alcohol in Solution B is 15%, so the amount of alcohol in Solution B used will be (15/100)x.
According to the problem, the resulting mixture has 125 milliliters of pure alcohol.
So, the equation we can set up is:
(10/100)(x - 500) + (15/100)x = 125
To solve this equation, we can simplify it:
(0.10x - 50) + (0.15x) = 125
0.10x - 50 + 0.15x = 125
0.25x - 50 = 125
0.25x = 125 + 50
0.25x = 175
x = 175 / 0.25
x = 700
Therefore, Mary uses 700 milliliters of Solution B.