in the lab, tom has two solutions that contain alcohol and is mixing them with each other. he uses 300 millilters less of solution A than solution B. solution A is 10% alcohol and solution B is 13% alcohol. How many millilters of solution B does he use, if the resulting mixture has 269 millilters of pure alcohol?

Question

in the lab, tom has two solutions that contain alcohol and is mixing them with each other. he uses 300 millilters less of solution A than solution B. solution A is 10% alcohol and solution B is 13% alcohol. How many millilters of solution B does he use, if the resulting mixture has 269 millilters of pure alcohol?

Answer 1

To find the amount of solution B used, we can start by assigning variables to the unknowns. Let's say the amount of solution B used is x milliliters.

Since Tom uses 300 milliliters less of solution A than solution B, the amount of solution A used would be (x - 300) milliliters.

Now, let's calculate the total amount of alcohol in the resulting mixture:

The amount of alcohol in solution A = (x - 300) * 0.10
The amount of alcohol in solution B = x * 0.13

Since the resulting mixture has 269 milliliters of pure alcohol, we can set up the following equation:

(x - 300) * 0.10 + x * 0.13 = 269

Now we can solve for x:

0.10x - 30 + 0.13x = 269
0.23x - 30 = 269
0.23x = 299
x = 299 / 0.23
x ≈ 1,300

So, Tom used approximately 1,300 milliliters of solution B.

Answer 2

let Vb be the volume of solution B

Va*.1+Vb*.13=269

(Vb-300)*.1+Vb*.13=269
solve for Vb