Answer :
To solve the problem of determining which ratios are equivalent to the ratio of 6 eggs to 1 tablespoon of butter, let's break it down step by step.
1. Understanding the Initial Ratio:
- The initial ratio given is 6 eggs for every 1 tablespoon of butter. This can be written as a fraction: [tex]\( \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].
2. Evaluate Each Given Ratio:
Let's compare each ratio provided in the question to [tex]\( \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex] to see if they are equivalent.
- First Ratio: [tex]\( \frac{12 \text{ eggs}}{2 \text{ tbsp}} \)[/tex]
Simplifying this ratio:
[tex]\[
\frac{12 \text{ eggs}}{2 \text{ tbsp}} = \frac{12 \div 2}{2 \div 2} = \frac{6 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
This is equivalent to the initial ratio.
- Second Ratio: [tex]\( \frac{15 \text{ eggs}}{3 \text{ tbsp}} \)[/tex]
Simplifying this ratio:
[tex]\[
\frac{15 \text{ eggs}}{3 \text{ tbsp}} = \frac{15 \div 3}{3 \div 3} = \frac{5 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
This is not equivalent to the initial ratio.
- Third Ratio: [tex]\( \frac{24 \text{ eggs}}{4 \text{ tbsp}} \)[/tex]
Simplifying this ratio:
[tex]\[
\frac{24 \text{ eggs}}{4 \text{ tbsp}} = \frac{24 \div 4}{4 \div 4} = \frac{6 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
This is equivalent to the initial ratio.
- Fourth Ratio: [tex]\( \frac{9 \text{ eggs}}{1.5 \text{ tbsp}} \)[/tex]
Simplifying this ratio:
[tex]\[
\frac{9 \text{ eggs}}{1.5 \text{ tbsp}} = \frac{9 \div 1.5}{1.5 \div 1.5} = \frac{6 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
This is equivalent to the initial ratio.
3. Conclusion:
- The ratios that are equivalent to the initial ratio [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 are the ratios that correctly match the initial requirement for making the quiche.
1. Understanding the Initial Ratio:
- The initial ratio given is 6 eggs for every 1 tablespoon of butter. This can be written as a fraction: [tex]\( \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex].
2. Evaluate Each Given Ratio:
Let's compare each ratio provided in the question to [tex]\( \frac{6 \text{ eggs}}{1 \text{ tbsp}} \)[/tex] to see if they are equivalent.
- First Ratio: [tex]\( \frac{12 \text{ eggs}}{2 \text{ tbsp}} \)[/tex]
Simplifying this ratio:
[tex]\[
\frac{12 \text{ eggs}}{2 \text{ tbsp}} = \frac{12 \div 2}{2 \div 2} = \frac{6 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
This is equivalent to the initial ratio.
- Second Ratio: [tex]\( \frac{15 \text{ eggs}}{3 \text{ tbsp}} \)[/tex]
Simplifying this ratio:
[tex]\[
\frac{15 \text{ eggs}}{3 \text{ tbsp}} = \frac{15 \div 3}{3 \div 3} = \frac{5 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
This is not equivalent to the initial ratio.
- Third Ratio: [tex]\( \frac{24 \text{ eggs}}{4 \text{ tbsp}} \)[/tex]
Simplifying this ratio:
[tex]\[
\frac{24 \text{ eggs}}{4 \text{ tbsp}} = \frac{24 \div 4}{4 \div 4} = \frac{6 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
This is equivalent to the initial ratio.
- Fourth Ratio: [tex]\( \frac{9 \text{ eggs}}{1.5 \text{ tbsp}} \)[/tex]
Simplifying this ratio:
[tex]\[
\frac{9 \text{ eggs}}{1.5 \text{ tbsp}} = \frac{9 \div 1.5}{1.5 \div 1.5} = \frac{6 \text{ eggs}}{1 \text{ tbsp}}
\][/tex]
This is equivalent to the initial ratio.
3. Conclusion:
- The ratios that are equivalent to the initial ratio [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 are the ratios that correctly match the initial requirement for making the quiche.
