Answer :
To solve the given problem, we need to perform the calculations across two primary steps: determining the percentage of food each flock consumed and then using these percentages to simulate the number of birds in each flock.
### Step 1: Calculate the Food Percentage for Each Flock
We need to find out what percentage of the total 300 pieces of food each flock has consumed.
- Flock X:
- Pieces of food consumed: 123
- [tex]\( \text{Food Percentage} = \left( \frac{\text{Flock X food}}{\text{Total Pieces of Food}} \right) \times 100 = \left( \frac{123}{300} \right) \times 100 = 41.0\% \)[/tex]
- Flock Y:
- Pieces of food consumed: 99
- [tex]\( \text{Food Percentage} = \left( \frac{\text{Flock Y food}}{\text{Total Pieces of Food}} \right) \times 100 = \left( \frac{99}{300} \right) \times 100 = 33.0\% \)[/tex]
- Flock Z:
- Pieces of food consumed: 78
- [tex]\( \text{Food Percentage} = \left( \frac{\text{Flock Z food}}{\text{Total Pieces of Food}} \right) \times 100 = \left( \frac{78}{300} \right) \times 100 = 26.0\% \)[/tex]
So, filling in the table for food percentage, we get:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline \multirow{3}{*}{\begin{tabular}{l} Total Pieces of Food Eaten \\ (from previous page) \end{tabular}} & \multirow[b]{2}{}{ Flock $X$} & \multirow[b]{2}{}{ Flock Y } & \multirow[b]{2}{*}{ Flock Z } \\ \hline & & & \\ \hline & 123 & 99 & 78 \\ \hline Food Percentage* & 41.0\% & 33.0\% & 26.0\% \\ \hline Simulated Number of Birds & $\square$ & $\square$ & \\ \hline \end{tabular} \][/tex]
### Step 2: Calculate the Simulated Number of Birds for Each Flock
Now, using the food percentages calculated above, we determine the simulated number of birds for each flock. Given that the total number of birds is 30:
- Flock X:
- [tex]\( \text{Simulated Number of Birds} = \left( \frac{\text{Flock X Percentage}}{100} \right) \times \text{Total Number of Birds} = \left( \frac{41.0}{100} \right) \times 30 = 12.3 \)[/tex]
- Flock Y:
- [tex]\( \text{Simulated Number of Birds} = \left( \frac{\text{Flock Y Percentage}}{100} \right) \times \text{Total Number of Birds} = \left( \frac{33.0}{100} \right) \times 30 = 9.9 \)[/tex]
- Flock Z:
- [tex]\( \text{Simulated Number of Birds} = \left( \frac{\text{Flock Z Percentage}}{100} \right) \times \text{Total Number of Birds} = \left( \frac{26.0}{100} \right) \times 30 = 7.8 \)[/tex]
So, the final table with the simulated number of birds would look like this:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline \multirow{3}{*}{\begin{tabular}{l} Total Pieces of Food Eaten \\ (from previous page) \end{tabular}} & \multirow[b]{2}{}{ Flock $X$} & \multirow[b]{2}{}{ Flock Y } & \multirow[b]{2}{*}{ Flock Z } \\ \hline & & & \\ \hline & 123 & 99 & 78 \\ \hline Food Percentage* & 41.0\% & 33.0\% & 26.0\% \\ \hline Simulated Number of Birds & 12.3 & 9.9 & 7.8 \\ \hline \end{tabular} \][/tex]
We have now completely filled out the table with the calculated percentages and the simulated number of birds.
### Step 1: Calculate the Food Percentage for Each Flock
We need to find out what percentage of the total 300 pieces of food each flock has consumed.
- Flock X:
- Pieces of food consumed: 123
- [tex]\( \text{Food Percentage} = \left( \frac{\text{Flock X food}}{\text{Total Pieces of Food}} \right) \times 100 = \left( \frac{123}{300} \right) \times 100 = 41.0\% \)[/tex]
- Flock Y:
- Pieces of food consumed: 99
- [tex]\( \text{Food Percentage} = \left( \frac{\text{Flock Y food}}{\text{Total Pieces of Food}} \right) \times 100 = \left( \frac{99}{300} \right) \times 100 = 33.0\% \)[/tex]
- Flock Z:
- Pieces of food consumed: 78
- [tex]\( \text{Food Percentage} = \left( \frac{\text{Flock Z food}}{\text{Total Pieces of Food}} \right) \times 100 = \left( \frac{78}{300} \right) \times 100 = 26.0\% \)[/tex]
So, filling in the table for food percentage, we get:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline \multirow{3}{*}{\begin{tabular}{l} Total Pieces of Food Eaten \\ (from previous page) \end{tabular}} & \multirow[b]{2}{}{ Flock $X$} & \multirow[b]{2}{}{ Flock Y } & \multirow[b]{2}{*}{ Flock Z } \\ \hline & & & \\ \hline & 123 & 99 & 78 \\ \hline Food Percentage* & 41.0\% & 33.0\% & 26.0\% \\ \hline Simulated Number of Birds & $\square$ & $\square$ & \\ \hline \end{tabular} \][/tex]
### Step 2: Calculate the Simulated Number of Birds for Each Flock
Now, using the food percentages calculated above, we determine the simulated number of birds for each flock. Given that the total number of birds is 30:
- Flock X:
- [tex]\( \text{Simulated Number of Birds} = \left( \frac{\text{Flock X Percentage}}{100} \right) \times \text{Total Number of Birds} = \left( \frac{41.0}{100} \right) \times 30 = 12.3 \)[/tex]
- Flock Y:
- [tex]\( \text{Simulated Number of Birds} = \left( \frac{\text{Flock Y Percentage}}{100} \right) \times \text{Total Number of Birds} = \left( \frac{33.0}{100} \right) \times 30 = 9.9 \)[/tex]
- Flock Z:
- [tex]\( \text{Simulated Number of Birds} = \left( \frac{\text{Flock Z Percentage}}{100} \right) \times \text{Total Number of Birds} = \left( \frac{26.0}{100} \right) \times 30 = 7.8 \)[/tex]
So, the final table with the simulated number of birds would look like this:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline \multirow{3}{*}{\begin{tabular}{l} Total Pieces of Food Eaten \\ (from previous page) \end{tabular}} & \multirow[b]{2}{}{ Flock $X$} & \multirow[b]{2}{}{ Flock Y } & \multirow[b]{2}{*}{ Flock Z } \\ \hline & & & \\ \hline & 123 & 99 & 78 \\ \hline Food Percentage* & 41.0\% & 33.0\% & 26.0\% \\ \hline Simulated Number of Birds & 12.3 & 9.9 & 7.8 \\ \hline \end{tabular} \][/tex]
We have now completely filled out the table with the calculated percentages and the simulated number of birds.
