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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 }}{15 \text{ tbsp }}[/tex]

Answer :

To solve this problem, we need to start with the basic ratio provided in the question: 6 eggs to 1 tablespoon of butter. This can be written as the ratio [tex]\( \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].

Now, let's examine the given options to determine which are equivalent to this ratio:

1. Option 1: [tex]\( \frac{12 \text{ eggs}}{2 \text{ tbsp}} \)[/tex]
- Simplify this ratio by dividing both the numerator and the denominator by 2:
[tex]\[
\frac{12 \div 2}{2 \div 2} = \frac{6 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
- This is identical to the given ratio of 6 eggs to 1 tablespoon, so it is equivalent.

2. Option 2: [tex]\( \frac{15 \text{ eggs}}{3 \text{ tbsp}} \)[/tex]
- Simplify this ratio by dividing both the numerator and the denominator by 3:
[tex]\[
\frac{15 \div 3}{3 \div 3} = \frac{5 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
- This is not equivalent to the ratio of 6 eggs to 1 tablespoon.

3. Option 3: [tex]\( \frac{24 \text{ eggs}}{4 \text{ tbsp}} \)[/tex]
- Simplify this ratio by dividing both the numerator and the denominator by 4:
[tex]\[
\frac{24 \div 4}{4 \div 4} = \frac{6 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
- This is also identical to the given ratio of 6 eggs to 1 tablespoon, so it is equivalent.

4. Option 4: [tex]\( \frac{9 \text{ eggs}}{15 \text{ tbsp}} \)[/tex]
- Simplify this ratio by dividing both the numerator and the denominator by 3:
[tex]\[
\frac{9 \div 3}{15 \div 3} = \frac{3 \text{ eggs}}{5 \text{ tbsp}}
\][/tex]
- This is not equivalent to the ratio of 6 eggs to 1 tablespoon.

From this analysis, 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]

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Rewritten by : Barada

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