Let's go through the solution step by step as requested.
Step 1: Calculate the Food Percentage for Each Flock
Divide each flock's total pieces of food by the total number of pieces of food eaten (300).
- For Flock X:
[tex]\[
\text{Food Percentage for Flock X} = \frac{147}{300} = 0.49
\][/tex]
- For Flock Y:
[tex]\[
\text{Food Percentage for Flock Y} = \frac{93}{300} = 0.31
\][/tex]
- For Flock Z:
[tex]\[
\text{Food Percentage for Flock Z} = \frac{60}{300} = 0.2
\][/tex]
Now, we have the food percentages:
- Flock X: 0.49
- Flock Y: 0.31
- Flock Z: 0.2
Step 2: Calculate the Simulated Number of Birds in Each Flock for the 3rd Generation
Multiply the food percentage for each flock by the total number of birds (30).
- For Flock X:
[tex]\[
\text{Simulated Number of Birds in Flock X} = 0.49 \times 30 = 14.7
\][/tex]
- For Flock Y:
[tex]\[
\text{Simulated Number of Birds in Flock Y} = 0.31 \times 30 = 9.3
\][/tex]
- For Flock Z:
[tex]\[
\text{Simulated Number of Birds in Flock Z} = 0.2 \times 30 = 6.0
\][/tex]
The simulated number of birds for each flock in the 3rd generation are:
- Flock X: 14.7
- Flock Y: 9.3
- Flock Z: 6.0
Summary in Table
[tex]\[
\begin{array}{|l|l|l|l|}
\cline{2-4}
\multicolumn{1}{c|}{} & \text{Flock X} & \text{Flock Y} & \text{Flock Z} \\
\hline
\text{Total Pieces of Food Eaten} & 147 & 93 & 60 \\
\hline
\text{Food Percentage} & 0.49 & 0.31 & 0.2 \\
\hline
\begin{array}{l}
\text{Simulated Number of Birds in Flock} \\
\text{for 3rd Generation}
\end{array} & 14.7 & 9.3 & 6.0 \\
\hline
\end{array}
\][/tex]
