Answer :
To solve this problem, we want to compare the ratio of eggs to tablespoons of butter. The initial given ratio is 6 eggs to 1 tablespoon of butter. We need to find which of the provided ratios are equivalent to this initial ratio.
An equivalent ratio means that both ratios represent the same relationship between the two quantities. To determine if two ratios are equivalent, we can check if the proportion between the numbers in one ratio is the same as the proportion in the other ratio.
Let's examine each provided ratio:
1. The ratio of 12 eggs to 2 tablespoons of butter:
- We simplify this by dividing both sides by 2.
- [tex]\( \frac{12 \text{ eggs}}{2 \text{ tbsp}} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex]
- This is the same as the initial ratio (6:1), so this ratio is equivalent.
2. The ratio of 15 eggs to 3 tablespoons of butter:
- Simplifying this by dividing both sides by 3.
- [tex]\( \frac{15 \text{ eggs}}{3 \text{ tbsp}} = \frac{5 \text{ eggs}}{1 \text{ tbsp}} \)[/tex]
- This is not the same as the initial ratio (6:1), so this ratio is not equivalent.
3. The ratio of 24 eggs to 4 tablespoons of butter:
- Simplifying this by dividing both sides by 4.
- [tex]\( \frac{24 \text{ eggs}}{4 \text{ tbsp}} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex]
- This matches the initial ratio (6:1), so this ratio is equivalent.
4. The ratio of 9 eggs to 1.5 tablespoons of butter:
- Simplifying this by dividing both sides by 1.5.
- [tex]\( \frac{9 \text{ eggs}}{1.5 \text{ tbsp}} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex]
- This also matches the initial ratio (6:1), so this ratio is equivalent.
Therefore, the equivalent ratios to the initial 6 eggs to 1 tablespoon of butter 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]
These three ratios are equivalent to the initial given ratio, while the ratio of 15 eggs to 3 tablespoons is not.
An equivalent ratio means that both ratios represent the same relationship between the two quantities. To determine if two ratios are equivalent, we can check if the proportion between the numbers in one ratio is the same as the proportion in the other ratio.
Let's examine each provided ratio:
1. The ratio of 12 eggs to 2 tablespoons of butter:
- We simplify this by dividing both sides by 2.
- [tex]\( \frac{12 \text{ eggs}}{2 \text{ tbsp}} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex]
- This is the same as the initial ratio (6:1), so this ratio is equivalent.
2. The ratio of 15 eggs to 3 tablespoons of butter:
- Simplifying this by dividing both sides by 3.
- [tex]\( \frac{15 \text{ eggs}}{3 \text{ tbsp}} = \frac{5 \text{ eggs}}{1 \text{ tbsp}} \)[/tex]
- This is not the same as the initial ratio (6:1), so this ratio is not equivalent.
3. The ratio of 24 eggs to 4 tablespoons of butter:
- Simplifying this by dividing both sides by 4.
- [tex]\( \frac{24 \text{ eggs}}{4 \text{ tbsp}} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex]
- This matches the initial ratio (6:1), so this ratio is equivalent.
4. The ratio of 9 eggs to 1.5 tablespoons of butter:
- Simplifying this by dividing both sides by 1.5.
- [tex]\( \frac{9 \text{ eggs}}{1.5 \text{ tbsp}} = \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex]
- This also matches the initial ratio (6:1), so this ratio is equivalent.
Therefore, the equivalent ratios to the initial 6 eggs to 1 tablespoon of butter 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]
These three ratios are equivalent to the initial given ratio, while the ratio of 15 eggs to 3 tablespoons is not.
