Answer :
To solve this problem, we need to determine which of the given ratios are equivalent to the original ratio of 6 eggs to 1 tablespoon of butter. This is a simple matter of comparing ratios to see if they express the same relationship.
1. Original Ratio:
The original ratio given is 6 eggs for every 1 tablespoon of butter. We can express this ratio as 6:1 or as a fraction [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
2. Comparing Ratios:
We need to check each given ratio to see if it equals the original ratio of 6:1.
- First Ratio [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]:
Simplifying this fraction gives [tex]\(\frac{12}{2} = 6\)[/tex]. Since this matches the original ratio, it is equivalent.
- Second Ratio [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]:
Simplifying this fraction gives [tex]\(\frac{15}{3} = 5\)[/tex]. This does not match the original ratio, so it is not equivalent.
- Third Ratio [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]:
Simplifying this fraction gives [tex]\(\frac{24}{4} = 6\)[/tex]. Since this matches the original ratio, it is equivalent.
- Fourth Ratio [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]:
Simplifying this fraction gives [tex]\(\frac{9}{1.5} = 6\)[/tex]. Since this matches the original ratio, it is equivalent.
3. Conclusion:
The ratios that are equivalent to the original ratio of 6 eggs to 1 tablespoon 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].
So, the equivalent ratios 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]
1. Original Ratio:
The original ratio given is 6 eggs for every 1 tablespoon of butter. We can express this ratio as 6:1 or as a fraction [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
2. Comparing Ratios:
We need to check each given ratio to see if it equals the original ratio of 6:1.
- First Ratio [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]:
Simplifying this fraction gives [tex]\(\frac{12}{2} = 6\)[/tex]. Since this matches the original ratio, it is equivalent.
- Second Ratio [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]:
Simplifying this fraction gives [tex]\(\frac{15}{3} = 5\)[/tex]. This does not match the original ratio, so it is not equivalent.
- Third Ratio [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]:
Simplifying this fraction gives [tex]\(\frac{24}{4} = 6\)[/tex]. Since this matches the original ratio, it is equivalent.
- Fourth Ratio [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]:
Simplifying this fraction gives [tex]\(\frac{9}{1.5} = 6\)[/tex]. Since this matches the original ratio, it is equivalent.
3. Conclusion:
The ratios that are equivalent to the original ratio of 6 eggs to 1 tablespoon 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].
So, the equivalent ratios 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]
