To determine the correct statement, let's analyze the given data and ratios.
The mixtures consist of:
- Solution A and Solution B in the ratio of 4:2. This simplifies to 2:1.
Calculating the total mixture for the examples in the table:
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For 4 cups of Solution A and 2 cups of Solution B:
- Total mixture = 4 + 2 = 6 cups
- Ratio of Solution A to the total mixture = 4:6, which simplifies to 2:3.
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For 8 cups of Solution A and 4 cups of Solution B:
- Total mixture = 8 + 4 = 12 cups
- Ratio of Solution A to the total mixture = 8:12, which simplifies to 2:3.
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For 12 cups of Solution A and 6 cups of Solution B:
- Total mixture = 12 + 6 = 18 cups
- Ratio of Solution A to the total mixture = 12:18, which simplifies to 2:3.
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For 16 cups of Solution A and 8 cups of Solution B:
- Total mixture = 16 + 8 = 24 cups
- Ratio of Solution A to the total mixture = 16:24, which simplifies to 2:3.
Now, let's evaluate each statement:
A. There are 3 cups of solution A for every 6 cups of the mixture.
- False (as we found the ratio A to mixture is 2:3, not 3:6).
B. For each cup of solution A, there are 2 cups of solution B.
- False (the ratio is actually 2 cups of A for every 1 cup of B).
C. The ratio of the number of cups of solution A to the total number of cups of the mixture is 3:2.
- False (it's actually 2:3).
D. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3.
- True (as demonstrated by our calculations).
Therefore, the correct statement is:
D. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3.
11 answers