Let's solve this step-by-step:
1. Find the Food Percentage for Flock X:
The total pieces of food eaten is 300. Flock X has eaten 147 pieces of food. To find the percentage of food eaten by Flock X, we use the formula:
[tex]\[
\text{Food Percentage for Flock X} = \left( \frac{\text{Food Eaten by Flock X}}{\text{Total Food Eaten}} \right) \times 100
\][/tex]
[tex]\[
\text{Food Percentage for Flock X} = \left( \frac{147}{300} \right) \times 100 = 49\%
\][/tex]
2. Verify Food Percentage for Flock Y:
It is given that the food percentage for Flock Y is already 7%.
3. Find the Food Percentage for Flock Z:
Flock Z has eaten 60 pieces of food. Using the same formula, we find the percentage of food eaten by Flock Z.
[tex]\[
\text{Food Percentage for Flock Z} = \left( \frac{60}{300} \right) \times 100 = 20\%
\][/tex]
Now, the table with the Food Percentages filled in looks like this:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & \text{Flock X} & \text{Flock Y} & \text{Flock Z} \\
\hline
\begin{tabular}{l}
Total Pieces of Food Eaten \\
\text{(from previous page)}
\end{tabular} & 147 & 93 & 60 \\
\hline \text{Food Percentage} & 49\% & 7\% & 20\% \\
\hline \begin{tabular}{l}
Simulated Number of Birds in Flock \\
for 3rd Generation
\end{tabular} & & & $\square$ \\
\hline
\end{tabular}
\][/tex]
4. Simulated Number of Birds in Flock Z for the Third Generation:
To find the simulated number of birds in Flock Z, we multiply the food percentage for each flock by the total number of birds (30):
[tex]\[
\text{Simulated Number of Birds in Flock Z} = \left( \frac{\text{Food Percentage Z}}{100} \right) \times \text{Total Number of Birds}
\][/tex]
[tex]\[
\text{Simulated Number of Birds in Flock Z} = \left( \frac{20}{100} \right) \times 30 = 6
\][/tex]
Finally, the completed table will look like this:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & \text{Flock X} & \text{Flock Y} & \text{Flock Z} \\
\hline
\begin{tabular}{l}
Total Pieces of Food Eaten \\
\text{(from previous page)}
\end{tabular} & 147 & 93 & 60 \\
\hline \text{Food Percentage} & 49\% & 7\% & 20\% \\
\hline \begin{tabular}{l}
Simulated Number of Birds in Flock \\
for 3rd Generation
\end{tabular} & & & 6 \\
\hline
\end{tabular}
\][/tex]
