Let's detail step-by-step how to solve the problem:
### Step 1: Calculate the Food Percentage for Each Flock
The first step is to determine what percentage of the total food each flock has eaten. Given:
- Total food eaten by all flocks combined: 300 pieces
- Food eaten by Flock [tex]\(X\)[/tex]: 57 pieces
- Food eaten by Flock [tex]\(Y\)[/tex]: 153 pieces
- Food eaten by Flock [tex]\(Z\)[/tex]: 90 pieces
To find the food percentage for each flock, use the formula:
[tex]\[
\text{Food Percentage} = \left( \frac{\text{Food Eaten by Flock}}{\text{Total Food Eaten}} \right) \times 100
\][/tex]
Applying this formula:
[tex]\[
\text{Food Percentage for Flock } X = \left( \frac{57}{300} \right) \times 100 = 19\%
\][/tex]
[tex]\[
\text{Food Percentage for Flock } Y = \left( \frac{153}{300} \right) \times 100 = 51\%
\][/tex]
[tex]\[
\text{Food Percentage for Flock } Z = \left( \frac{90}{300} \right) \times 100 = 30\%
\][/tex]
### Step 2: Calculate the Number of Birds in Each Flock
Next, we need to calculate how many birds are represented by the food percentage in each flock, given that the total number of birds is 30.
To find the number of birds in each flock, use the formula:
[tex]\[
\text{Number of Birds in Flock} = \left( \frac{\text{Food Percentage}}{100} \right) \times \text{Total Number of Birds}
\][/tex]
Applying this formula:
[tex]\[
\text{Number of Birds in Flock } X = \left( \frac{19}{100} \right) \times 30 = 5.7
\][/tex]
[tex]\[
\text{Number of Birds in Flock } Y = \left( \frac{51}{100} \right) \times 30 = 15.3
\][/tex]
[tex]\[
\text{Number of Birds in Flock } Z = \left( \frac{30}{100} \right) \times 30 = 9.0
\][/tex]
### Summary of Results
- The food percentage consumed by Flock [tex]\(X\)[/tex] is [tex]\(19\%\)[/tex], corresponding to [tex]\(5.7\)[/tex] birds.
- The food percentage consumed by Flock [tex]\(Y\)[/tex] is [tex]\(51\%\)[/tex], corresponding to [tex]\(15.3\)[/tex] birds.
- The food percentage consumed by Flock [tex]\(Z\)[/tex] is [tex]\(30\%\)[/tex], corresponding to [tex]\(9.0\)[/tex] birds.
Thus, the completed table will look like:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
& Flock X & Flock Y & Flock Z \\
\hline
Total Pieces of Food Eaten & 57 & 153 & 90 \\
\hline
Food Percentage & 19\% & 51\% & 30\% \\
\hline
Simulated Number of Birds in Flock & 5.7 & 15.3 & 9.0 \\
\hline
\end{tabular}
\][/tex]
