Let's solve this problem step-by-step.
### Step 1: Calculate the Food Percentage for Each Flock
Given:
- Total pieces of food eaten by all flocks: 300
- Pieces of food eaten by Flock [tex]$X$[/tex]: 147
- Pieces of food eaten by Flock [tex]$Y$[/tex]: 93
- Pieces of food eaten by Flock [tex]$Z$[/tex]: 60
To find the food percentage for each flock, we divide the number of pieces eaten by each flock by the total number of pieces of food.
#### For Flock [tex]$X$[/tex]:
[tex]\[ \text{Food Percentage for Flock } X = \frac{147}{300} \][/tex]
The calculation reveals:
[tex]\[ \text{Food Percentage for Flock } X = 0.49 = 49\% \][/tex]
#### For Flock [tex]$Y$[/tex]:
[tex]\[ \text{Food Percentage for Flock } Y = \frac{93}{300} \][/tex]
The calculation reveals:
[tex]\[ \text{Food Percentage for Flock } Y = 0.31 = 31\% \][/tex]
#### For Flock [tex]$Z$[/tex]:
[tex]\[ \text{Food Percentage for Flock } Z = \frac{60}{300} \][/tex]
The calculation reveals:
[tex]\[ \text{Food Percentage for Flock } Z = 0.20 = 20\% \][/tex]
### Step 2: Simulate the Number of Birds in Each Flock for the 3rd Generation
Given:
- Total number of birds: 30
- Food percentage for each flock from the previous calculations
We multiply the food percentage for each flock by the total number of birds to find the simulated number of birds in each flock for the 3rd generation.
#### For Flock [tex]$X$[/tex]:
[tex]\[ \text{Simulated Number of Birds for Flock } X = 0.49 \times 30 \][/tex]
The calculation reveals:
[tex]\[ \text{Simulated Number of Birds for Flock } X = 14.7 \][/tex]
#### For Flock [tex]$Y$[/tex]:
[tex]\[ \text{Simulated Number of Birds for Flock } Y = 0.31 \times 30 \][/tex]
The calculation reveals:
[tex]\[ \text{Simulated Number of Birds for Flock } Y = 9.3 \][/tex]
#### For Flock [tex]$Z$[/tex]:
[tex]\[ \text{Simulated Number of Birds for Flock } Z = 0.20 \times 30 \][/tex]
The calculation reveals:
[tex]\[ \text{Simulated Number of Birds for Flock } Z = 6.0 \][/tex]
### Final Results
| | Flock [tex]$X$[/tex] | Flock [tex]$Y$[/tex] | Flock [tex]$Z$[/tex] |
|----------------------|-----------|-----------|-----------|
| Total Pieces of Food Eaten | 147 | 93 | 60 |
| Food Percentage | 49% | 31% | 20% |
| Simulated Number of Birds in Flock | 14.7 | 9.3 | 6.0 |
This completes the detailed, step-by-step solution for calculating the food percentage and simulated number of birds in each flock for the 3rd generation.
