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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 understand the basic ratio given in the question: for every 1 tablespoon of butter, you need 6 eggs. This ratio of eggs to tablespoons of butter can be written as [tex]\( \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].

Now, we have to determine which of the provided ratios are equivalent to this original ratio. Let's review each option:

1. [tex]\(\frac{12 \text{ eggs}}{2 \text{ tbsp}}\)[/tex]:
- Simplify this ratio: [tex]\( \frac{12}{2} = 6 \)[/tex].
- This is equivalent to the base ratio [tex]\( \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].

2. [tex]\(\frac{15 \text{ eggs}}{3 \text{ tbsp}}\)[/tex]:
- Simplify this ratio: [tex]\( \frac{15}{3} = 5 \)[/tex].
- This is not equivalent to the base ratio.

3. [tex]\(\frac{24 \text{ eggs}}{4 \text{ tbsp}}\)[/tex]:
- Simplify this ratio: [tex]\( \frac{24}{4} = 6 \)[/tex].
- This is equivalent to the base ratio [tex]\( \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].

4. [tex]\(\frac{9 \text{ eggs}}{1.5 \text{ tbsp}}\)[/tex]:
- Simplify this ratio: [tex]\( \frac{9}{1.5} = 6 \)[/tex].
- This is equivalent to the base ratio [tex]\( \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].

Therefore, the ratios that are equivalent to the initial ratio of [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]

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Rewritten by : Barada