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

A. [tex]\frac{12 \text{ eggs }}{2 \text{ tbsp }}[/tex]
B. [tex]\frac{15 \text{ eggs }}{3 \text{ tbsp }}[/tex]
C. [tex]\frac{24 \text{ eggs }}{4 \text{ tbsp }}[/tex]
D. [tex]\frac{9 \text{ eggs }}{1.5 \text{ tbsp }}[/tex]

Answer :

To solve the problem of determining which ratios are equivalent to the given ratio of 1 tablespoon of butter for every 6 eggs, we'll compare each ratio to see if it matches the initial condition.

### Step-by-step Solution:

1. Initial Ratio:
- The basic ratio is 1 tablespoon (tbsp) of butter for every 6 eggs.

2. Equivalent Ratios:
- To find equivalent ratios, each ratio should have the same "egg per tablespoon" relationship as 6 eggs per 1 tablespoon.

3. Examine Each Given Ratio:

- Option 1: [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]
- Calculate the ratio: [tex]\( \frac{12 \text{ eggs}}{2 \text{ tbsp}} = \frac{12}{2} = 6 \)[/tex]
- This matches the initial ratio (6 eggs per tablespoon), so this ratio is equivalent.

- Option 2: [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]
- Calculate the ratio: [tex]\( \frac{15 \text{ eggs}}{3 \text{ tbsp}} = \frac{15}{3} = 5 \)[/tex]
- This does not match the initial ratio, so this ratio is not equivalent.

- Option 3: [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]
- Calculate the ratio: [tex]\( \frac{24 \text{ eggs}}{4 \text{ tbsp}} = \frac{24}{4} = 6 \)[/tex]
- This matches the initial ratio, so this ratio is equivalent.

- Option 4: [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]
- Calculate the ratio: [tex]\( \frac{9 \text{ eggs}}{1.5 \text{ tbsp}} = \frac{9}{1.5} = 6 \)[/tex]
- This matches the initial ratio, so this ratio is equivalent.

### Conclusion:
The ratios that are equivalent to the initial ratio of 1 tablespoon of butter for every 6 eggs 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 equivalent ratios are the first, third, and fourth options.