Mateo's pasta sauce recipe uses 8 tomatoes for every 3 teaspoons of oil. Select all of the true statements. A. The recipe uses $$ \frac{3}{8} $$ teaspoons of oil per tomato. B. The recipe uses $$ \frac{3}{8} $$ tomatoes per teaspoon of oil. C. He needs 3 tomatoes for every 8 teaspoons of oil. De needs $$ \frac{3}{4} $$ teaspoons of oil for every 2 tomatoes. He needs 9 tomatoes for every 4 teaspoons of oil.

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UpStudy AI · Accepted Answer

Let's analyze each statement based on Mateo's pasta sauce recipe, which uses 8 tomatoes for every 3 teaspoons of oil.

1. **Statement A**: The recipe uses $$ \frac{3}{8} $$ teaspoons of oil per tomato.
   - To find the amount of oil per tomato, we divide the amount of oil by the number of tomatoes:
     $$
     \text{Oil per tomato} = \frac{3 \text{ teaspoons}}{8 \text{ tomatoes}} = \frac{3}{8} \text{ teaspoons per tomato}
     $$
   - This statement is **true**.

2. **Statement B**: The recipe uses $$ \frac{3}{8} $$ tomatoes per teaspoon of oil.
   - To find the number of tomatoes per teaspoon of oil, we divide the number of tomatoes by the amount of oil:
     $$
     \text{Tomatoes per teaspoon} = \frac{8 \text{ tomatoes}}{3 \text{ teaspoons}} = \frac{8}{3} \text{ tomatoes per teaspoon}
     $$
   - This statement is **false**.

3. **Statement C**: He needs 3 tomatoes for every 8 teaspoons of oil.
   - According to the recipe, he needs 8 tomatoes for 3 teaspoons of oil. This means:
     $$
     \text{For 8 teaspoons of oil, he would need} = \frac{8 \text{ tomatoes}}{3 \text{ teaspoons}} \times 8 \text{ teaspoons} = \frac{64}{3} \text{ tomatoes} \approx 21.33 \text{ tomatoes}
     $$
   - This statement is **false**.

Now, let's analyze the additional statements:

4. **Statement D**: He needs $$ \frac{3}{4} $$ teaspoons of oil for every 2 tomatoes.
   - To find the amount of oil for 2 tomatoes, we can set up a proportion based on the original recipe:
     $$
     \text{Oil for 2 tomatoes} = \frac{3 \text{ teaspoons}}{8 \text{ tomatoes}} \times 2 \text{ tomatoes} = \frac{6}{8} \text{ teaspoons} = \frac{3}{4} \text{ teaspoons}
     $$
   - This statement is **true**.

5. **Statement E**: He needs 9 tomatoes for every 4 teaspoons of oil.
   - Using the original recipe, we can find how many tomatoes are needed for 4 teaspoons of oil:
     $$
     \text{Tomatoes for 4 teaspoons} = \frac{8 \text{ tomatoes}}{3 \text{ teaspoons}} \times 4 \text{ teaspoons} = \frac{32}{3} \text{ tomatoes} \approx 10.67 \text{ tomatoes}
     $$
   - This statement is **false**.

In summary, the true statements are:
- A. The recipe uses $$ \frac{3}{8} $$ teaspoons of oil per tomato.
- D. He needs $$ \frac{3}{4} $$ teaspoons of oil for every 2 tomatoes.
A. The recipe uses $$ \frac{3}{8} $$ teaspoons of oil per tomato. D. He needs $$ \frac{3}{4} $$ teaspoons of oil for every 2 tomatoes.

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