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How much water should be added to 20 ounces of a 15% solution of alcohol to dilute it to a 10% solution?

A) 2 ounces
B) 3 ounces
C) 4 ounces
D) 5 ounces

2 Answers

4 votes

Final Answer:

To dilute the 15% alcohol solution to 10%, you must add 10 ounces of water. None of the given options is answer.

Step-by-step explanation:

Calculate the amount of alcohol in the initial solution: 20 ounces * 15% = 3 ounces.

Let x be the number of ounces of water added.

The total amount of solution after dilution is 20 ounces + x ounces.

The final amount of alcohol remains the same, so 3 ounces = 0.1 * (20 + x) ounces.

Solve for x: 3 = 2 + 0.1x, 1 = 0.1x, x = 10 ounces.

Therefore, you need to add 10 ounces of water to achieve the desired 10% alcohol solution.

None of the given options is answer.

User CTarczon
by
8.9k points
1 vote

Final answer:

The calculation shows that to dilute a 15% alcohol solution to a 10% solution by adding water, 10 ounces of water is needed, but this option is not available in the provided choices, which may indicate an error in the question.

Step-by-step explanation:

The student wishes to dilute a 15% alcohol solution to a 10% solution. To solve this, we need to know the amount of pure alcohol in the original solution first, which is 15% of 20 ounces. This can be calculated as 0.15 × 20 ounces = 3 ounces of alcohol. The amount of alcohol remains the same after dilution, but the total volume of the solution changes. If we let x be the number of ounces of water to be added to achieve a 10% alcohol solution, the new total volume would be 20 ounces + x. The equation representing the dilution is (3 ounces) / (20 ounces + x) = 10% or 0.10.

Now, solving for x, we get:
3 / (20 + x) = 0.10
3 = 0.10 × (20 + x)
3 = 2 + 0.10x
3 - 2 = 0.10x
1 = 0.10x
x = 10 ounces.

However, none of the provided answer options suggests adding 10 ounces. Therefore, there may be an error in the question as the only logical answer based on the calculations made is 10 ounces of water, which is not listed in the options. The student may need to recheck the question or the answer options provided.

User Dharvik Shah
by
7.6k points

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