Sure, let's break down the solution step-by-step.
Step 1: Calculate the food percentage for each flock.
The total pieces of food eaten by all the flocks is 300 pieces. Each flock's food percentage is calculated by the formula:
[tex]\[ \text{Percentage of food eaten} = \left( \frac{\text{Pieces of food eaten by the flock}}{\text{Total pieces of food}} \right) \times 100 \][/tex]
- For Flock [tex]\(X\)[/tex]:
[tex]\[
\text{Percentage of food eaten by Flock } X = \left( \frac{57}{300} \right) \times 100 = 19.0\%
\][/tex]
- For Flock [tex]\(Y\)[/tex]:
[tex]\[
\text{Percentage of food eaten by Flock } Y = \left( \frac{153}{300} \right) \times 100 = 51.0\%
\][/tex]
- For Flock [tex]\(Z\)[/tex]:
[tex]\[
\text{Percentage of food eaten by Flock } Z = \left( \frac{90}{300} \right) \times 100 = 30.0\%
\][/tex]
Step 2: Calculate the simulated number of birds in each flock for the 2nd generation.
The total number of birds is 30. The number of birds in each flock for the 2nd generation is calculated by the formula:
[tex]\[ \text{Number of birds in flock for 2nd generation} = \left( \frac{\text{Percentage of food eaten by the flock}}{100} \right) \times \text{Total number of birds} \][/tex]
- For Flock [tex]\(X\)[/tex]:
[tex]\[
\text{Number of birds in Flock } X = \left( \frac{19.0}{100} \right) \times 30 = 5.7 \ (\text{birds})
\][/tex]
- For Flock [tex]\(Y\)[/tex]:
[tex]\[
\text{Number of birds in Flock } Y = \left( \frac{51.0}{100} \right) \times 30 = 15.3 \ (\text{birds})
\][/tex]
- For Flock [tex]\(Z\)[/tex]:
[tex]\[
\text{Number of birds in Flock } Z = \left( \frac{30.0}{100} \right) \times 30 = 9.0 \ (\text{birds})
\][/tex]
Putting it all together:
[tex]\[
\begin{tabular}{|l|l|l|l|}
\hline & Flock $X$ & Flock $Y$ & Flock $Z$ \\
\hline Total Pieces of Food Eaten & 57 & 153 & 90 \\
\hline Food Percentage* & 19.0\% & 51.0\% & 30.0\% \\
\hline Simulated Number of Birds in Flock for 2nd Generation & 5.7 & 15.3 & 9.0 \\
\hline
\end{tabular}
\][/tex]
So the percentages are 19.0%, 51.0% and 30.0% respectively and the simulated number of birds are 5.7, 15.3, and 9.0 respectively for flocks X, Y, and Z.
