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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 identifying which ratios are equivalent to the original ratio of 6 eggs to 1 tablespoon of butter, let's examine each option one by one. The base ratio given is 6:1, meaning for every 6 eggs, you use 1 tablespoon of butter.

We need to check each ratio to see if it simplifies to the same 6:1 ratio. Let's evaluate each:

1. Ratio: 12 eggs to 2 tablespoons
- Simplify: Divide 12 eggs by 2 tablespoons.
- Calculation: [tex]\( \frac{12}{2} = 6 \)[/tex]
- This simplifies to 6:1, which is equivalent to the original ratio.

2. Ratio: 15 eggs to 3 tablespoons
- Simplify: Divide 15 eggs by 3 tablespoons.
- Calculation: [tex]\( \frac{15}{3} = 5 \)[/tex]
- This simplifies to 5:1, which is not equivalent to the original ratio of 6:1.

3. Ratio: 24 eggs to 4 tablespoons
- Simplify: Divide 24 eggs by 4 tablespoons.
- Calculation: [tex]\( \frac{24}{4} = 6 \)[/tex]
- This simplifies to 6:1, which is equivalent to the original ratio.

4. Ratio: 9 eggs to 1.5 tablespoons
- Simplify: Divide 9 eggs by 1.5 tablespoons.
- Calculation: [tex]\( \frac{9}{1.5} = 6 \)[/tex]
- This simplifies to 6:1, which is equivalent to the original ratio.

Therefore, the ratios that are equivalent to 6:1 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]

Those are the correct equivalent ratios.

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Rewritten by : Barada