Sylvia Byrd

2022-07-06

In the lab, there are two solutions that contain alcohol and Yolanda is mixing them with each other. Solution A is 12% alcohol and Solution B is 40% alcohol. She uses 800 milliliters of Solution A. Find how many milliliters of Solution B does she use, if the resulting mixture is a 24% alcohol solution?

Jamiya Costa

Expert

Let solution B be V_B
The sum of alcohol in solution A and solution B is equal to the quantity of alcohol in the mixture of solution A and solution B.
Thus, the sum of 12% alcohol in solution A and 40% of alcohol in solution B is equal to the 24% of alcohol in the mixture of solution A and solution B.
$\frac{12}{100}\left({V}_{A}\right)+\frac{40}{100}\left({V}_{B}\right)=\frac{24}{100}\left({V}_{A}+{V}_{B}\right)$
Now, substitute the value of ${V}_{A}=800ml$ in the equation above:
$\frac{12}{100}\left({V}_{A}\right)+\frac{40}{100}\left({V}_{B}\right)=\frac{24}{100}\left({V}_{A}+{V}_{B}\right)$
$\frac{12}{100}\left(800ml\right)+\frac{40}{100}\left({V}_{B}\right)=\frac{24}{100}\left(800ml+{V}_{B}\right)$
$96ml+\frac{40}{100}\left({V}_{B}\right)=192ml+\frac{24}{100}\left({V}_{B}\right)$
$96ml+\frac{40}{100}\left({V}_{B}\right)-96ml=192ml+\frac{24}{100}\left({V}_{B}\right)-96ml$
$\frac{40}{100}\left({V}_{B}\right)=96ml+\frac{24}{100}\left({V}_{B}\right)$
$\frac{40}{100}\left({V}_{B}\right)-\frac{24}{100}\left({V}_{B}\right)=96ml+\frac{24}{100}\left({V}_{B}\right)-\frac{24}{100}\left({V}_{B}\right)$
$\frac{16}{100}\left({V}_{B}\right)=96ml$
$\frac{100}{16}×\frac{16}{100}\left({V}_{B}\right)=\frac{100}{16}×96ml$
${V}_{B}=600ml$

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