\begin{tabular}{|l|l|l|l|}
\hline
\begin{tabular}{l}
Total Pieces of Food Eaten \\
(from previous page)
\end{tabular} & Flock X & Flock Y & Flock Z \\
\hline Food Percentage & 123 & 99 & 78 \\
\hline Simulated Number of Birds in Flock for 2nd Generation & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] \\
\hline
\end{tabular}

Divide each flock's total pieces of food by 300, the total number of pieces of food eaten.
Multiply the food percentage for each flock by the total number of birds (30).



Answer :

To determine the simulated number of birds in each flock for the 2nd generation, follow these detailed steps:

1. Determine the Total Pieces of Food Eaten by Each Flock:

Use the given food percentage values to find out the total pieces of food eaten by each flock. We'll assume the pieces of food eaten by each flock as [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] respectively.

2. Calculate the Proportion of Food Each Flock Ate:

The problem statement directs us to divide the total pieces of food eaten by each flock by 300 (the total number of pieces of food eaten).

[tex]\[ \text{Proportion for Flock X} = \frac{123}{300} \][/tex]
[tex]\[ \text{Proportion for Flock Y} = \frac{99}{300} \][/tex]
[tex]\[ \text{Proportion for Flock Z} = \frac{78}{300} \][/tex]

3. Calculate the Simulated Number of Birds in Each Flock:

Next, we multiply the obtained proportion for each flock by the total number of birds, which is 30.

[tex]\[ \text{Number of Birds in Flock X} = \left(\frac{123}{300}\right) \times 30 \][/tex]
[tex]\[ \text{Number of Birds in Flock Y} = \left(\frac{99}{300}\right) \times 30 \][/tex]
[tex]\[ \text{Number of Birds in Flock Z} = \left(\frac{78}{300}\right) \times 30 \][/tex]

4. Simplify the Calculations:

Carrying out the multiplications:
[tex]\[ \text{Number of Birds in Flock X} = \left(\frac{123}{300}\right) \times 30 = \left(\frac{123 \times 30}{300}\right) = \left(\frac{3690}{300}\right) = 12.3 \][/tex]
[tex]\[ \text{Number of Birds in Flock Y} = \left(\frac{99}{300}\right) \times 30 = \left(\frac{99 \times 30}{300}\right) = \left(\frac{2970}{300}\right) = 9.9 \][/tex]
[tex]\[ \text{Number of Birds in Flock Z} = \left(\frac{78}{300}\right) \times 30 = \left(\frac{78 \times 30}{300}\right) = \left(\frac{2340}{300}\right) = 7.8 \][/tex]

Given these steps, the simulated number of birds in each flock for the second generation can be summarized as follows:
- Flock X: 12.3 birds
- Flock Y: 9.9 birds
- Flock Z: 7.8 birds