Answer :
To solve the problem of finding equivalent ratios for making a quiche, let's first understand the original ratio provided: 1 tablespoon of butter for every 6 eggs. This can be written as a ratio of eggs to tablespoons: [tex]\(6:1\)[/tex].
Now, we need to check which of the given ratios are equivalent to this original ratio:
1. Ratio [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]:
- Calculate the ratio by dividing the number of eggs by the number of tablespoons: [tex]\( \frac{12}{2} = 6 \)[/tex].
- Since this equals the original ratio of 6 eggs per tablespoon, this ratio is equivalent.
2. Ratio [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]:
- Calculate the ratio: [tex]\( \frac{15}{3} = 5 \)[/tex].
- This does not equal the original ratio of 6, so this ratio is not equivalent.
3. Ratio [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]:
- Calculate the ratio: [tex]\( \frac{24}{4} = 6 \)[/tex].
- This equals the original ratio of 6, making this ratio equivalent.
4. Ratio [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]:
- Calculate the ratio: [tex]\( \frac{9}{1.5} = 6 \)[/tex].
- Since this also equals the original ratio of 6, this ratio is equivalent.
Therefore, the ratios that are equivalent to the original ratio [tex]\(6:1\)[/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]
Now, we need to check which of the given ratios are equivalent to this original ratio:
1. Ratio [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]:
- Calculate the ratio by dividing the number of eggs by the number of tablespoons: [tex]\( \frac{12}{2} = 6 \)[/tex].
- Since this equals the original ratio of 6 eggs per tablespoon, this ratio is equivalent.
2. Ratio [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]:
- Calculate the ratio: [tex]\( \frac{15}{3} = 5 \)[/tex].
- This does not equal the original ratio of 6, so this ratio is not equivalent.
3. Ratio [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]:
- Calculate the ratio: [tex]\( \frac{24}{4} = 6 \)[/tex].
- This equals the original ratio of 6, making this ratio equivalent.
4. Ratio [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]:
- Calculate the ratio: [tex]\( \frac{9}{1.5} = 6 \)[/tex].
- Since this also equals the original ratio of 6, this ratio is equivalent.
Therefore, the ratios that are equivalent to the original ratio [tex]\(6:1\)[/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]
