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.
### 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.
