Let's tackle the problem step-by-step.
1. Total Pieces of Food Eaten:
- Flock X: 57 pieces
- Flock Y: 153 pieces
- Flock Z: 90 pieces
2. Total Pieces of Food:
- Total pieces eaten by all birds: 300 pieces
3. Food Percentage:
To find the food percentage for each flock, we divide the number of pieces of food each flock ate by the total number of pieces of food, and then multiply by 100 to get the percentage:
- For Flock X:
[tex]\[
\text{Food Percentage for Flock X} = \left( \frac{57}{300} \right) \times 100 = 19\%
\][/tex]
- For Flock Y:
[tex]\[
\text{Food Percentage for Flock Y} = \left( \frac{153}{300} \right) \times 100 = 51\%
\][/tex]
- For Flock Z:
The percentage is already given as 7%.
4. Simulated Number of Birds in Flock for the 2nd Generation:
To determine the number of birds in each flock for the second generation, we multiply the food percentage each flock received by the total number of birds (30).
- For Flock X:
[tex]\[
\text{Simulated Birds for Flock X} = \left( \frac{19}{100} \right) \times 30 = 5.7
\][/tex]
- For Flock Y:
[tex]\[
\text{Simulated Birds for Flock Y} = \left( \frac{51}{100} \right) \times 30 = 15.3
\][/tex]
- For Flock Z:
[tex]\[
\text{Simulated Birds for Flock Z} = \left( \frac{7}{100} \right) \times 30 = 2.1
\][/tex]
Putting it all together, we can fill out the table as follows:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
& \text{Flock X} & \text{Flock Y} & \text{Flock Z} \\
\hline
\text{Total Pieces of Food Eaten} & 57 & 153 & 90 \\
\hline
\text{Food Percentage}^* & 19\% & 51\% & 7\% \\
\hline
\text{Simulated Number of Birds in Flock for 2nd Generation}^*& 5.7 & 15.3 & 2.1 \\
\hline
\end{array}
\][/tex]
Thus, Flock X has 19% of the total food, resulting in 5.7 birds for the next generation; Flock Y has 51% of the total food, resulting in 15.3 birds; and Flock Z has 7% of the total food, resulting in 2.1 birds.
