Question

Three containers contain alcohol to water in the ratios 3:5, 1:3, and 1:1 respectively. If the solutions of the three containers are mixed in the volume ratio of 1:2:3, then what is the ratio of alcohol to water in the final solution?

• A. 5:9
• B. 6:7
• C. 12:19
• D. 19:29

Hint:

When mixing solutions with different concentrations, use the volume ratios to find the individual amounts of alcohol and water, then calculate the overall ratio.

Answer 1

The Correct Option is B

Step 1: Take the volumes from the three containers as \( x, 2x, 3x \), matching the given ratio \( 1:2:3 \).
Step 2: Find the alcohol and water contributed by each container using their respective ratios, \( 3:5 \), \( 1:3 \), and \( 1:1 \).
Step 3: Add the alcohol contributions together and the water contributions together, then simplify the resulting ratio.
\[ \text{Alcohol} : \text{Water} = 6 : 7 \]
Therefore, the correct answer is 6:7.

Answer 2

A convenient way to avoid fractions is to assume a total mixing volume that divides evenly by the ratio parts and the container ratios, then compute alcohol and water in whole numbers.

1. Setting up whole-number volumes: Taking the three containers' volumes in a convenient multiple of the ratio \( 1:2:3 \) lets the alcohol-to-water splits of \( 3:5 \), \( 1:3 \), and \( 1:1 \) be computed without fractions.
2. Adding alcohol from each container: Summing the whole-number alcohol amounts from all three containers gives the total alcohol in the final mixture.
3. Adding water from each container: Summing the whole-number water amounts from all three containers gives the total water in the final mixture.
4. Forming the ratio: Dividing the total alcohol by the total water and simplifying gives the final ratio in its lowest terms.

Working through the whole-number version of the calculation gives the same simplified ratio as before.

Therefore, the correct answer is 6:7.