Sure, let's walk through this problem step-by-step.
We already know the total pieces of food eaten and the total number of birds. We're asked to:
1. Calculate the percentage of total food eaten by each flock.
2. Determine the number of birds in the next generation based on the percentage of food they ate.
Step 1: Calculate Percentage of Food Eaten
We calculate the percentage of total food eaten by each flock as follows:
- Flock [tex]\(X\)[/tex]:
- Total pieces of food: 57
- Total pieces of food eaten by all flocks: 300
- Percentage: [tex]\(\frac{57}{300} \times 100 = 19\%\)[/tex]
- Flock [tex]\(Y\)[/tex]:
- Total pieces of food: 153
- Total pieces of food eaten by all flocks: 300
- Percentage: [tex]\(\frac{153}{300} \times 100 = 51\%\)[/tex]
- Flock [tex]\(Z\)[/tex]:
- Total pieces of food: 90
- Total pieces of food eaten by all flocks: 300
- Percentage: [tex]\(\frac{90}{300} \times 100 = 30\%\)[/tex]
So, the percentages are:
- Flock [tex]\(X\)[/tex]: 19%
- Flock [tex]\(Y\)[/tex]: 51%
- Flock [tex]\(Z\)[/tex]: 30%
Step 2: Calculate Number of Birds in Next Generation
Next, we multiply the food percentage by the total number of birds (30) to find out how many birds each flock will have in the second generation.
- Flock [tex]\(X\)[/tex]:
- Percentage of food: 19%
- Number of birds in second generation: [tex]\(\frac{19}{100} \times 30 = 5.7\)[/tex] birds
- Flock [tex]\(Y\)[/tex]:
- Percentage of food: 51%
- Number of birds in second generation: [tex]\(\frac{51}{100} \times 30 = 15.3\)[/tex] birds
- Flock [tex]\(Z\)[/tex]:
- Percentage of food: 30%
- Number of birds in second generation: [tex]\(\frac{30}{100} \times 30 = 9\)[/tex] birds
Hence, the number of birds in the second generation for each flock are as follows:
- Flock [tex]\(X\)[/tex]: 5.7 birds
- Flock [tex]\(Y\)[/tex]: 15.3 birds
- Flock [tex]\(Z\)[/tex]: 9 birds
From these results, we can see:
- Flock [tex]\(Y\)[/tex] was the most successful at feeding, so it will have the greatest number in the second generation.
- Flock [tex]\(X\)[/tex] was the least successful at feeding and has shrunk the most.
