Answer :
To compare the quantities for making a quiche, we start by determining the given ratio of eggs to tablespoons of butter. The problem states that you need 1 tablespoon of butter for every 6 eggs. This establishes the original ratio as:
[tex]\[ \frac{6 \text{ eggs}}{1 \text{ tbsp}} \][/tex]
Now, we want to determine which of the given ratios are equivalent to this original ratio:
1. Ratio: [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]
- Simplify the ratio: [tex]\( \frac{12}{2} = 6 \)[/tex]
- This ratio is equal to the original ratio of 6 eggs per tablespoon.
2. Ratio: [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]
- Simplify the ratio: [tex]\( \frac{15}{3} = 5 \)[/tex]
- This is not equal to the original ratio, so it is not equivalent.
3. Ratio: [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]
- Simplify the ratio: [tex]\( \frac{24}{4} = 6 \)[/tex]
- This ratio is equal to the original ratio, making it equivalent.
4. Ratio: [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]
- Simplify the ratio: [tex]\( \frac{9}{1.5} = 6 \)[/tex]
- This ratio equals 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]
[tex]\[ \frac{6 \text{ eggs}}{1 \text{ tbsp}} \][/tex]
Now, we want to determine which of the given ratios are equivalent to this original ratio:
1. Ratio: [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]
- Simplify the ratio: [tex]\( \frac{12}{2} = 6 \)[/tex]
- This ratio is equal to the original ratio of 6 eggs per tablespoon.
2. Ratio: [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]
- Simplify the ratio: [tex]\( \frac{15}{3} = 5 \)[/tex]
- This is not equal to the original ratio, so it is not equivalent.
3. Ratio: [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]
- Simplify the ratio: [tex]\( \frac{24}{4} = 6 \)[/tex]
- This ratio is equal to the original ratio, making it equivalent.
4. Ratio: [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]
- Simplify the ratio: [tex]\( \frac{9}{1.5} = 6 \)[/tex]
- This ratio equals 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]
