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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.

A. [tex]\(\frac{12 \text{ eggs }}{2 \text{ tbsp }}\)[/tex]

B. [tex]\(\frac{15 \text{ eggs }}{3 \text{ tbsp }}\)[/tex]

C. [tex]\(\frac{24 \text{ eggs }}{4 \text{ tbsp }}\)[/tex]

D. [tex]\(\frac{9 \text{ eggs }}{1.5 \text{ tbsp }}\)[/tex]

Answer :

To solve the problem of identifying which ratios are equivalent to the given ratio of eggs to tablespoons of butter, follow these steps:

1. Understand the original ratio: The original ratio given in the problem is 6 eggs for every 1 tablespoon of butter. This can be written as the ratio [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].

2. Compare the provided ratios to the original:

- First ratio: [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]
- Simplify this ratio: [tex]\(12 \div 2 = 6\)[/tex] and [tex]\(2 \div 2 = 1\)[/tex].
- The simplified ratio is [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex], which is equivalent to the original ratio.

- Second ratio: [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]
- Simplify this ratio: [tex]\(15 \div 3 = 5\)[/tex] and [tex]\(3 \div 3 = 1\)[/tex].
- The simplified ratio is [tex]\(\frac{5 \text{ eggs}}{1 \text{ tbsp}}\)[/tex], which is different from the original ratio.

- Third ratio: [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]
- Simplify this ratio: [tex]\(24 \div 4 = 6\)[/tex] and [tex]\(4 \div 4 = 1\)[/tex].
- The simplified ratio is [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex], which matches the original ratio.

- Fourth ratio: [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]
- Simplify this ratio: [tex]\(\frac{9 \div 1.5 = 6}{1.5 \div 1.5 = 1}\)[/tex].
- The simplified ratio is [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex], which is equivalent to the original ratio.

3. Conclusion: Based on the simplifications:
- The ratios [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] are equivalent to the original ratio of [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].
- The ratio [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex] is not equivalent.

Therefore, the equivalent ratios are the first, third, and fourth options.

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Rewritten by : Barada