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To make a quiche, you need 1 tablespoon of butter for every 6 eggs. Write a ratio that compares these two quantities.

Which ratios are equivalent to this ratio? Check all that apply.

- [tex]\(\frac{12 \text{ eggs }}{2 \text{ tbsp }}\)[/tex]
- [tex]\(\frac{15 \text{ eggs }}{3 \text{ tbsp }}\)[/tex]
- [tex]\(\frac{24 \text{ eggs }}{4 \text{ tbsp }}\)[/tex]
- [tex]\(\frac{9 \text{ eggs }}{1.5 \text{ tbsp }}\)[/tex]

Answer :

To solve this problem, we need to determine which of the given ratios are equivalent to the original ratio of 6 eggs to 1 tablespoon of butter. This is a simple matter of comparing ratios to see if they express the same relationship.

1. Original Ratio:
The original ratio given is 6 eggs for every 1 tablespoon of butter. We can express this ratio as 6:1 or as a fraction [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].

2. Comparing Ratios:
We need to check each given ratio to see if it equals the original ratio of 6:1.

- First Ratio [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]:
Simplifying this fraction gives [tex]\(\frac{12}{2} = 6\)[/tex]. Since this matches the original ratio, it is equivalent.

- Second Ratio [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]:
Simplifying this fraction gives [tex]\(\frac{15}{3} = 5\)[/tex]. This does not match the original ratio, so it is not equivalent.

- Third Ratio [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]:
Simplifying this fraction gives [tex]\(\frac{24}{4} = 6\)[/tex]. Since this matches the original ratio, it is equivalent.

- Fourth Ratio [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]:
Simplifying this fraction gives [tex]\(\frac{9}{1.5} = 6\)[/tex]. Since this matches the original ratio, it is equivalent.

3. Conclusion:
The ratios that are equivalent to the original ratio of 6 eggs to 1 tablespoon 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].

So, 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]

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Rewritten by : Barada