Sylvia Byrd

Answered

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?

Answer & Explanation

Jamiya Costa

Expert

2022-07-07Added 18 answers

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.

$\frac{12}{100}({V}_{A})+\frac{40}{100}({V}_{B})=\frac{24}{100}({V}_{A}+{V}_{B})$

Now, substitute the value of ${V}_{A}=800ml$ in the equation above:

$\frac{12}{100}({V}_{A})+\frac{40}{100}({V}_{B})=\frac{24}{100}({V}_{A}+{V}_{B})$

$\frac{12}{100}(800ml)+\frac{40}{100}({V}_{B})=\frac{24}{100}(800ml+{V}_{B})$

$96ml+\frac{40}{100}({V}_{B})=192ml+\frac{24}{100}({V}_{B})$

$96ml+\frac{40}{100}({V}_{B})-96ml=192ml+\frac{24}{100}({V}_{B})-96ml$

$\frac{40}{100}({V}_{B})=96ml+\frac{24}{100}({V}_{B})$

$\frac{40}{100}({V}_{B})-\frac{24}{100}({V}_{B})=96ml+\frac{24}{100}({V}_{B})-\frac{24}{100}({V}_{B})$

$\frac{16}{100}({V}_{B})=96ml$

$\frac{100}{16}\times \frac{16}{100}({V}_{B})=\frac{100}{16}\times 96ml$

${V}_{B}=600ml$

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.

$\frac{12}{100}({V}_{A})+\frac{40}{100}({V}_{B})=\frac{24}{100}({V}_{A}+{V}_{B})$

Now, substitute the value of ${V}_{A}=800ml$ in the equation above:

$\frac{12}{100}({V}_{A})+\frac{40}{100}({V}_{B})=\frac{24}{100}({V}_{A}+{V}_{B})$

$\frac{12}{100}(800ml)+\frac{40}{100}({V}_{B})=\frac{24}{100}(800ml+{V}_{B})$

$96ml+\frac{40}{100}({V}_{B})=192ml+\frac{24}{100}({V}_{B})$

$96ml+\frac{40}{100}({V}_{B})-96ml=192ml+\frac{24}{100}({V}_{B})-96ml$

$\frac{40}{100}({V}_{B})=96ml+\frac{24}{100}({V}_{B})$

$\frac{40}{100}({V}_{B})-\frac{24}{100}({V}_{B})=96ml+\frac{24}{100}({V}_{B})-\frac{24}{100}({V}_{B})$

$\frac{16}{100}({V}_{B})=96ml$

$\frac{100}{16}\times \frac{16}{100}({V}_{B})=\frac{100}{16}\times 96ml$

${V}_{B}=600ml$

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