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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 the problem of finding the equivalent ratios, let's first establish the base ratio given in the problem. You need 1 tablespoon of butter for every 6 eggs. This forms the ratio of eggs to tablespoons as [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].

Now, let's examine the provided ratios to determine if they are equivalent to [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex].

1. For [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]:
- Simplifying [tex]\(\frac{12}{2}\)[/tex] gives [tex]\(6\)[/tex].
- This simplified ratio is [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex], which matches the original ratio, so this is equivalent.

2. For [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]:
- Simplifying [tex]\(\frac{15}{3}\)[/tex] gives [tex]\(5\)[/tex].
- [tex]\(\frac{5 \text{ eggs}}{1 \text{ tbsp}}\)[/tex] does not match [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex], so this is not equivalent.

3. For [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]:
- Simplifying [tex]\(\frac{24}{4}\)[/tex] gives [tex]\(6\)[/tex].
- This simplifies to [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex], which matches the original ratio, so this is equivalent.

4. For [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]:
- Simplifying [tex]\(\frac{9}{1.5}\)[/tex] gives [tex]\(6\)[/tex].
- This simplifies to [tex]\(\frac{6 \text{ eggs}}{1 \text{ tbsp}}\)[/tex], which matches the original ratio, so this is equivalent.

After evaluating each ratio, the equivalent ratios 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]

These three ratios align with the original given ratio.

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Rewritten by : Barada