To determine which statements are correct, let's calculate the ratios of smoothie size to the number of mangos used for Angela, Kim, and Bri based on the given data.
1. Angela:
- Mangos used: [tex]\(1\)[/tex]
- Smoothie size: [tex]\(90 \, \text{oz}\)[/tex]
- Ratio: [tex]\(\frac{90 \, \text{oz}}{1 \, \text{mango}} = 90.0\)[/tex]
2. Kim:
- Mangos used: [tex]\(3\)[/tex]
- Smoothie size: [tex]\(270 \, \text{oz}\)[/tex]
- Ratio: [tex]\(\frac{270 \, \text{oz}}{3 \, \text{mangos}} = 90.0\)[/tex]
3. Bri:
- Mangos used: [tex]\(4\)[/tex]
- Smoothie size: [tex]\(36 \, \text{oz}\)[/tex]
- Ratio: [tex]\(\frac{36 \, \text{oz}}{4 \, \text{mangos}} = 9.0\)[/tex]
Now, let's analyze each statement based on the calculated ratios:
1. Statement 1: "The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela."
- Correct. Both ratios for Angela and Kim are [tex]\(90.0\)[/tex].
2. Statement 2: "The ratio of smoothie size to mangos used for Kim is 1.9, and the ratio of smoothie size to mangos used for Bri is [tex]\(4: 27\)[/tex]."
- Incorrect. The ratio of smoothie size to mangos used for Kim is [tex]\(90.0\)[/tex], not [tex]\(1.9\)[/tex]. Additionally, the ratio for Bri is [tex]\(\frac{36 \, \text{oz}}{4 \, \text{mangos}} = 9.0\)[/tex], not [tex]\(4: 27\)[/tex].
3. Statement 3: "The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim."
- Incorrect. Both ratios are the same at [tex]\(90.0\)[/tex].
4. Statement 4: "The ratio of smoothie size to mangos used for Bri is 9.1, and the ratio of smoothie size to mangos used for Angela is [tex]\(4: 36\)[/tex]."
- Incorrect. The ratio for Bri is [tex]\(9.0\)[/tex], not [tex]\(9.1\)[/tex]. Additionally, the ratio for Angela is [tex]\(\frac{90 \, \text{oz}}{1 \, \text{mango}} = 90.0\)[/tex], not [tex]\(4: 36\)[/tex].
Hence, the correct statement is: "The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela."
