Answer :
To find the ratio of eggs to tablespoons of butter and then determine which provided ratios are equivalent, here's how we can tackle it:
1. Understand the given ratio: The recipe calls for 1 tablespoon (tbsp) of butter for every 6 eggs. This gives us the ratio of [tex]\( \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].
2. Check the provided ratios for equivalence:
- Option 1: [tex]\( \frac{12 \text{ eggs}}{2 \text{ tbsp}} \)[/tex]:
- Simplify this ratio: [tex]\( \frac{12 \div 2}{2 \div 2} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].
- This matches the original ratio, so it is equivalent.
- Option 2: [tex]\( \frac{15 \text{ eggs}}{3 \text{ tbsp}} \)[/tex]:
- Simplify this ratio: [tex]\( \frac{15 \div 3}{3 \div 3} = \frac{5 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].
- This does not match our original ratio, so it is not equivalent.
- Option 3: [tex]\( \frac{24 \text{ eggs}}{4 \text{ tbsp}} \)[/tex]:
- Simplify this ratio: [tex]\( \frac{24 \div 4}{4 \div 4} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].
- This matches the original ratio, so it is equivalent.
- Option 4: [tex]\( \frac{9 \text{ eggs}}{1.5 \text{ tbsp}} \)[/tex]:
- Simplify this ratio: [tex]\( \frac{9 \div 1.5}{1.5 \div 1.5} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].
- This matches the original ratio, so it is equivalent.
Therefore, the ratios that are equivalent to [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]
1. Understand the given ratio: The recipe calls for 1 tablespoon (tbsp) of butter for every 6 eggs. This gives us the ratio of [tex]\( \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].
2. Check the provided ratios for equivalence:
- Option 1: [tex]\( \frac{12 \text{ eggs}}{2 \text{ tbsp}} \)[/tex]:
- Simplify this ratio: [tex]\( \frac{12 \div 2}{2 \div 2} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].
- This matches the original ratio, so it is equivalent.
- Option 2: [tex]\( \frac{15 \text{ eggs}}{3 \text{ tbsp}} \)[/tex]:
- Simplify this ratio: [tex]\( \frac{15 \div 3}{3 \div 3} = \frac{5 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].
- This does not match our original ratio, so it is not equivalent.
- Option 3: [tex]\( \frac{24 \text{ eggs}}{4 \text{ tbsp}} \)[/tex]:
- Simplify this ratio: [tex]\( \frac{24 \div 4}{4 \div 4} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].
- This matches the original ratio, so it is equivalent.
- Option 4: [tex]\( \frac{9 \text{ eggs}}{1.5 \text{ tbsp}} \)[/tex]:
- Simplify this ratio: [tex]\( \frac{9 \div 1.5}{1.5 \div 1.5} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].
- This matches the original ratio, so it is equivalent.
Therefore, the ratios that are equivalent to [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]
