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To make a quiche, you need 1 tablespoon of butter for every 6 eggs. Write a ratio that compares these two quantities. Which ratios are equivalent to this ratio? Check all that apply.

- [tex]\(\frac{12 \text{ eggs }}{2 \text{ tbsp }}\)[/tex]
- [tex]\(\frac{15 \text{ eggs }}{3 \text{ tbsp }}\)[/tex]
- [tex]\(\frac{24 \text{ eggs }}{4 \text{ tbsp }}\)[/tex]
- [tex]\(\frac{9 \text{ eggs }}{1.5 \text{ tbsp }}\)[/tex]

Answer :

To solve the problem of finding which ratios are equivalent, we start by identifying the basic ratio given in the problem. The question states that we need 1 tablespoon of butter for every 6 eggs. Therefore, the basic ratio of eggs to tablespoons of butter is:

[tex]\[ \frac{6 \text{ eggs}}{1 \text{ tbsp}} \][/tex]

Now, let's examine each of the provided ratios to see if they are equivalent to this basic ratio:

1. Ratio: [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]

- Calculation: [tex]\(\frac{12}{2} = 6\)[/tex] eggs per tbsp
- This ratio simplifies to 6 eggs per 1 tbsp, which is equivalent to the basic ratio.

2. Ratio: [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]

- Calculation: [tex]\(\frac{15}{3} = 5\)[/tex] eggs per tbsp
- This ratio simplifies to 5 eggs per 1 tbsp, which is not equivalent to the basic ratio.

3. Ratio: [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]

- Calculation: [tex]\(\frac{24}{4} = 6\)[/tex] eggs per tbsp
- This ratio simplifies to 6 eggs per 1 tbsp, which is equivalent to the basic ratio.

4. Ratio: [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]

- Calculation: [tex]\(\frac{9}{1.5} = 6\)[/tex] eggs per tbsp
- This ratio simplifies to 6 eggs per 1 tbsp, which is equivalent to the basic ratio.

After these comparisons, the equivalent ratios to the original [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex] are:

- [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]
- [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]
- [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]

Therefore, the ratios that are equivalent to the given ratio are: [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex], [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex], and [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex].

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