Answer :
To solve this problem, we need to understand how to compare ratios. The initial ratio given is 1 tablespoon of butter for every 6 eggs. We can express this as a ratio:
[tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
Now, let's compare this ratio to the provided options to determine which are equivalent:
1. [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]:
- Simplify this ratio:
[tex]\(\frac{12 \div 2}{2 \div 2} = \frac{6}{1}\)[/tex].
- This is equivalent to the original ratio [tex]\(\frac{6}{1}\)[/tex].
2. [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]:
- Simplify this ratio:
[tex]\(\frac{15 \div 3}{3 \div 3} = \frac{5}{1}\)[/tex].
- This is not equivalent to the original ratio [tex]\(\frac{6}{1}\)[/tex].
3. [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]:
- Simplify this ratio:
[tex]\(\frac{24 \div 4}{4 \div 4} = \frac{6}{1}\)[/tex].
- This is equivalent to the original ratio [tex]\(\frac{6}{1}\)[/tex].
4. [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]:
- Simplify this ratio:
[tex]\(\frac{9 \div 1.5}{1.5 \div 1.5} = \frac{6}{1}\)[/tex].
- This is equivalent to the original ratio [tex]\(\frac{6}{1}\)[/tex].
After comparing, 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]
On checking each option, these are the options where the ratios are equivalent to the original ratio of [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
[tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
Now, let's compare this ratio to the provided options to determine which are equivalent:
1. [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]:
- Simplify this ratio:
[tex]\(\frac{12 \div 2}{2 \div 2} = \frac{6}{1}\)[/tex].
- This is equivalent to the original ratio [tex]\(\frac{6}{1}\)[/tex].
2. [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]:
- Simplify this ratio:
[tex]\(\frac{15 \div 3}{3 \div 3} = \frac{5}{1}\)[/tex].
- This is not equivalent to the original ratio [tex]\(\frac{6}{1}\)[/tex].
3. [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]:
- Simplify this ratio:
[tex]\(\frac{24 \div 4}{4 \div 4} = \frac{6}{1}\)[/tex].
- This is equivalent to the original ratio [tex]\(\frac{6}{1}\)[/tex].
4. [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]:
- Simplify this ratio:
[tex]\(\frac{9 \div 1.5}{1.5 \div 1.5} = \frac{6}{1}\)[/tex].
- This is equivalent to the original ratio [tex]\(\frac{6}{1}\)[/tex].
After comparing, 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]
On checking each option, these are the options where the ratios are equivalent to the original ratio of [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
