Answer :
To solve the problem of finding which ratios are equivalent, we start by identifying the basic ratio given in the problem. The question states that we need 1 tablespoon of butter for every 6 eggs. Therefore, the basic ratio of eggs to tablespoons of butter is:
[tex]\[ \frac{6 \text{ eggs}}{1 \text{ tbsp}} \][/tex]
Now, let's examine each of the provided ratios to see if they are equivalent to this basic ratio:
1. Ratio: [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]
- Calculation: [tex]\(\frac{12}{2} = 6\)[/tex] eggs per tbsp
- This ratio simplifies to 6 eggs per 1 tbsp, which is equivalent to the basic ratio.
2. Ratio: [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]
- Calculation: [tex]\(\frac{15}{3} = 5\)[/tex] eggs per tbsp
- This ratio simplifies to 5 eggs per 1 tbsp, which is not equivalent to the basic ratio.
3. Ratio: [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]
- Calculation: [tex]\(\frac{24}{4} = 6\)[/tex] eggs per tbsp
- This ratio simplifies to 6 eggs per 1 tbsp, which is equivalent to the basic ratio.
4. Ratio: [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]
- Calculation: [tex]\(\frac{9}{1.5} = 6\)[/tex] eggs per tbsp
- This ratio simplifies to 6 eggs per 1 tbsp, which is equivalent to the basic ratio.
After these comparisons, the equivalent ratios to the original [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]
Therefore, the ratios that are equivalent to the given ratio 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].
[tex]\[ \frac{6 \text{ eggs}}{1 \text{ tbsp}} \][/tex]
Now, let's examine each of the provided ratios to see if they are equivalent to this basic ratio:
1. Ratio: [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]
- Calculation: [tex]\(\frac{12}{2} = 6\)[/tex] eggs per tbsp
- This ratio simplifies to 6 eggs per 1 tbsp, which is equivalent to the basic ratio.
2. Ratio: [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]
- Calculation: [tex]\(\frac{15}{3} = 5\)[/tex] eggs per tbsp
- This ratio simplifies to 5 eggs per 1 tbsp, which is not equivalent to the basic ratio.
3. Ratio: [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]
- Calculation: [tex]\(\frac{24}{4} = 6\)[/tex] eggs per tbsp
- This ratio simplifies to 6 eggs per 1 tbsp, which is equivalent to the basic ratio.
4. Ratio: [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]
- Calculation: [tex]\(\frac{9}{1.5} = 6\)[/tex] eggs per tbsp
- This ratio simplifies to 6 eggs per 1 tbsp, which is equivalent to the basic ratio.
After these comparisons, the equivalent ratios to the original [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]
Therefore, the ratios that are equivalent to the given ratio 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].
