Question

in the lab, jose has two solutions that contain alcohol and is mixing them with each other. he uses 300 milliliters less of solution a than solution b. solution a is 13% alcohol and solution b is 18% alcohol. how many milliliters of solution b does he use, if the resulting mixture has 178 milliliters of pure alcohol?
number of milliliters of solution b:

Explanation:

Step1: Define variables

Let $x$ = volume (mL) of Solution B. Then volume of Solution A = $x - 300$.

Step2: Set up alcohol equation

Alcohol from A + Alcohol from B = Total alcohol
$0.13(x - 300) + 0.18x = 178$

Step3: Expand and simplify

$0.13x - 39 + 0.18x = 178$
$0.31x - 39 = 178$

Step4: Solve for x

$0.31x = 178 + 39$
$0.31x = 217$
$x = \frac{217}{0.31}$
$x = 700$

Answer:

700