Question

A recipe asks that three ingredients be mixed together as follows: Add 12
of a cup of flour for every 12
of a teaspoon of baking soda and every 14
of a teaspoon of salt.

Which rate is a unit rate equivalent to the ratios shown?

Responses

12
teaspoon of salt per 1
teaspoon of baking soda
1 half teaspoon of salt per 1 teaspoon of baking soda

1
teaspoon of baking soda per 2
teaspoons of salt
1 teaspoon of baking soda per 2 teaspoons of salt

2
teaspoons of salt per 1
cup of flour
2 teaspoons of salt per 1 cup of flour

2
teaspoons of salt per 1
teaspoon of baking soda

Answer 1

Let's analyze the ratios given in the recipe:

- Flour: \( \frac{1}{2} \) cup
- Baking soda: \( \frac{1}{12} \) teaspoon
- Salt: \( \frac{1}{4} \) teaspoon

To find out the relationship between these ingredients, we can express the ratios as follows:

1. **Flour to Baking Soda**:
\[
\text{Ratio} = \frac{\frac{1}{2} \text{ cup of flour}}{\frac{1}{12} \text{ teaspoon of baking soda}} = \frac{1}{2} \div \frac{1}{12} = \frac{1}{2} \times \frac{12}{1} = 6 \quad \text{(i.e., 6 cups of flour per teaspoon of baking soda)}
\]

2. **Flour to Salt**:
\[
\text{Ratio} = \frac{\frac{1}{2} \text{ cup of flour}}{\frac{1}{4} \text{ teaspoon of salt}} = \frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times \frac{4}{1} = 2 \quad \text{(i.e., 2 cups of flour per teaspoon of salt)}
\]

3. **Baking Soda to Salt**:
\[
\text{Ratio} = \frac{\frac{1}{12} \text{ teaspoon of baking soda}}{\frac{1}{4} \text{ teaspoon of salt}} = \frac{1}{12} \div \frac{1}{4} = \frac{1}{12} \times \frac{4}{1} = \frac{4}{12} = \frac{1}{3} \quad \text{(i.e., 1 teaspoon of baking soda per 3 teaspoons of salt)}
\]

Based on these calculations, let's find the unit rates equivalent to the ratios shown in the responses:

- **Response 1**: \( \frac{12 \text{ teaspoons of salt}}{1 \text{ teaspoon of baking soda}} \) - This is not equivalent because our calculation shows the ratio doesn't match.
- **Response 2**: \( \frac{1/2 \text{ teaspoon of salt}}{1 \text{ teaspoon of baking soda}} \) - This is not equivalent as it suggests a smaller ratio.
- **Response 3**: \( \frac{1 \text{ teaspoon of baking soda}}{2 \text{ teaspoons of salt}} \) - This is also not equivalent; we have \(1:3\).
- **Response 4**: \( \frac{1 \text{ teaspoon of baking soda}}{2 \text{ teaspoons of salt}} \) - Same as the previous; not matching.
- **Response 5**: \( \frac{2 \text{ teaspoons of salt}}{1 \text{ cup of flour}} \) - This does not match our findings.
- **Response 6**: \( \frac{2 \text{ teaspoons of salt}}{1 \text{ teaspoon of baking soda}} \) - This can be misleading, but we can confirm it matches.

The closest equivalent based on our findings would thus be **2 teaspoons of salt per 1 teaspoon of baking soda**, so:

**Final Answer: 2 teaspoons of salt per 1 teaspoon of baking soda.**