Certainly! Let's work through the problem step-by-step based on the information given:
### Step 1: Calculate the Food Percentage for Each Flock
First, we need to determine what percentage of the total food each flock consumed. The total number of pieces of food is 300.
- Flock X: Consumed 32 pieces of food.
[tex]\[ \text{Flock X Percentage} = \left( \frac{32}{300} \right) \times 100 \approx 10.67\% \][/tex]
- Flock Y: Consumed 180 pieces of food.
[tex]\[ \text{Flock Y Percentage} = \left( \frac{180}{300} \right) \times 100 = 60.00\% \][/tex]
- Flock Z: Consumed 88 pieces of food.
[tex]\[ \text{Flock Z Percentage} = \left( \frac{88}{300} \right) \times 100 \approx 29.33\% \][/tex]
The table so far will look like this:
[tex]\[
\begin{tabular}{|l|l|l|l|}
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & Flock $X$ & Flock $Y$ & Flock $Z$ \\
\hline Total Pieces of Food Eaten & 32 & 180 & 88 \\
\hline Food Percentage & 10.67\% & 60.00\% & 29.33\% \\
\hline
\end{tabular}
\][/tex]
### Step 2: Calculate the Simulated Number of Birds in Each Flock for the 3rd Generation
Next, we use the food percentage to calculate the projected number of birds in each flock for the third generation. The total number of birds is 30.
- Flock X:
[tex]\[ \text{Flock X Birds} = \left( \frac{10.67}{100} \right) \times 30 \approx 3.2 \][/tex]
- Flock Y:
[tex]\[ \text{Flock Y Birds} = \left( \frac{60.00}{100} \right) \times 30 = 18.0 \][/tex]
- Flock Z:
[tex]\[ \text{Flock Z Birds} = \left( \frac{29.33}{100} \right) \times 30 \approx 8.8 \][/tex]
Now, incorporating these values, the complete table will look like this:
[tex]\[
\begin{tabular}{|l|l|l|l|}
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & Flock $X$ & Flock $Y$ & Flock $Z$ \\
\hline Total Pieces of Food Eaten & 32 & 180 & 88 \\
\hline Food Percentage & 10.67\% & 60.00\% & 29.33\% \\
\hline Simulated Number of Birds in Flock for 3rd Generation & 3.2 & 18.0 & 8.8 \\
\hline
\end{tabular}
\][/tex]
So, the detailed calculations show that Flock X constitutes approximately 10.67% of the food consumed and is projected to have around 3.2 birds; Flock Y constitutes 60.00% and is projected to have 18.0 birds; Flock Z constitutes approximately 29.33% and is projected to have around 8.8 birds in the third generation.
