Answer :
Certainly! Let's solve this step-by-step, ensuring to explain each part in detail, as it would be done in a classroom setting.
We have three flocks of birds: Flock [tex]\(X\)[/tex], Flock [tex]\(Y\)[/tex], and Flock [tex]\(Z\)[/tex]. We know the total pieces of food eaten by each flock as well as the total number of pieces of food eaten by all flocks combined. Our goal is to determine the food percentage for each flock and subsequently, the simulated number of birds in each flock for the 2nd generation.
Here's what we know:
- Total pieces of food eaten by Flock [tex]\(X\)[/tex] = 57
- Total pieces of food eaten by Flock [tex]\(Y\)[/tex] = 153
- Total pieces of food eaten by Flock [tex]\(Z\)[/tex] = 90
- Total pieces of food eaten by all flocks combined = 300
- Total number of birds in the 2nd generation = 30
### Step 1: Calculate the Food Percentage for Each Flock
To find the food percentage for each flock, we divide the total pieces of food eaten by that flock by the total pieces of food eaten by all the flocks combined (300). We then express it as a decimal fraction.
#### For Flock [tex]\(X\)[/tex]:
[tex]\[ \text{Food Percentage for Flock } X = \frac{\text{Total pieces of food eaten by Flock } X}{\text{Total pieces of food eaten by all flocks}} \][/tex]
[tex]\[ \text{Food Percentage for Flock } X = \frac{57}{300} \][/tex]
[tex]\[ \text{Food Percentage for Flock } X = 0.19 \][/tex]
#### For Flock [tex]\(Y\)[/tex]:
[tex]\[ \text{Food Percentage for Flock } Y = \frac{\text{Total pieces of food eaten by Flock } Y}{\text{Total pieces of food eaten by all flocks}} \][/tex]
[tex]\[ \text{Food Percentage for Flock } Y = \frac{153}{300} \][/tex]
[tex]\[ \text{Food Percentage for Flock } Y = 0.51 \][/tex]
#### For Flock [tex]\(Z\)[/tex]:
[tex]\[ \text{Food Percentage for Flock } Z = \frac{\text{Total pieces of food eaten by Flock } Z}{\text{Total pieces of food eaten by all flocks}} \][/tex]
[tex]\[ \text{Food Percentage for Flock } Z = \frac{90}{300} \][/tex]
[tex]\[ \text{Food Percentage for Flock } Z = 0.30 \][/tex]
### Step 2: Calculate the Simulated Number of Birds in Each Flock for the 2nd Generation
Now, we multiply the food percentage for each flock by the total number of birds (30) to find the simulated number of birds in each flock for the 2nd generation.
#### For Flock [tex]\(X\)[/tex]:
[tex]\[ \text{Simulated Number of Birds in Flock } X = \text{Food Percentage for Flock } X \times 30 \][/tex]
[tex]\[ \text{Simulated Number of Birds in Flock } X = 0.19 \times 30 \][/tex]
[tex]\[ \text{Simulated Number of Birds in Flock } X = 5.7 \][/tex]
#### For Flock [tex]\(Y\)[/tex]:
[tex]\[ \text{Simulated Number of Birds in Flock } Y = \text{Food Percentage for Flock } Y \times 30 \][/tex]
[tex]\[ \text{Simulated Number of Birds in Flock } Y = 0.51 \times 30 \][/tex]
[tex]\[ \text{Simulated Number of Birds in Flock } Y = 15.3 \][/tex]
#### For Flock [tex]\(Z\)[/tex]:
[tex]\[ \text{Simulated Number of Birds in Flock } Z = \text{Food Percentage for Flock } Z \times 30 \][/tex]
[tex]\[ \text{Simulated Number of Birds in Flock } Z = 0.30 \times 30 \][/tex]
[tex]\[ \text{Simulated Number of Birds in Flock } Z = 9.0 \][/tex]
### Summary
Let's summarize our results in the table.
\begin{tabular}{|l|l|l|l|}
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & Flock [tex]\(X\)[/tex] & Flock [tex]\(Y\)[/tex] & Flock [tex]\(Z\)[/tex] \\
\hline Total Pieces of Food Eaten & 57 & 153 & 90 \\
\hline Food Percentage & 0.19 & 0.51 & 0.30 \\
\hline Simulated Number of Birds in Flock for 2nd Generation & 5.7 & 15.3 & 9.0 \\
\hline
\end{tabular}
This completes our detailed step-by-step solution for calculating both the food percentages and the simulated number of birds in each flock for the 2nd generation.
We have three flocks of birds: Flock [tex]\(X\)[/tex], Flock [tex]\(Y\)[/tex], and Flock [tex]\(Z\)[/tex]. We know the total pieces of food eaten by each flock as well as the total number of pieces of food eaten by all flocks combined. Our goal is to determine the food percentage for each flock and subsequently, the simulated number of birds in each flock for the 2nd generation.
Here's what we know:
- Total pieces of food eaten by Flock [tex]\(X\)[/tex] = 57
- Total pieces of food eaten by Flock [tex]\(Y\)[/tex] = 153
- Total pieces of food eaten by Flock [tex]\(Z\)[/tex] = 90
- Total pieces of food eaten by all flocks combined = 300
- Total number of birds in the 2nd generation = 30
### Step 1: Calculate the Food Percentage for Each Flock
To find the food percentage for each flock, we divide the total pieces of food eaten by that flock by the total pieces of food eaten by all the flocks combined (300). We then express it as a decimal fraction.
#### For Flock [tex]\(X\)[/tex]:
[tex]\[ \text{Food Percentage for Flock } X = \frac{\text{Total pieces of food eaten by Flock } X}{\text{Total pieces of food eaten by all flocks}} \][/tex]
[tex]\[ \text{Food Percentage for Flock } X = \frac{57}{300} \][/tex]
[tex]\[ \text{Food Percentage for Flock } X = 0.19 \][/tex]
#### For Flock [tex]\(Y\)[/tex]:
[tex]\[ \text{Food Percentage for Flock } Y = \frac{\text{Total pieces of food eaten by Flock } Y}{\text{Total pieces of food eaten by all flocks}} \][/tex]
[tex]\[ \text{Food Percentage for Flock } Y = \frac{153}{300} \][/tex]
[tex]\[ \text{Food Percentage for Flock } Y = 0.51 \][/tex]
#### For Flock [tex]\(Z\)[/tex]:
[tex]\[ \text{Food Percentage for Flock } Z = \frac{\text{Total pieces of food eaten by Flock } Z}{\text{Total pieces of food eaten by all flocks}} \][/tex]
[tex]\[ \text{Food Percentage for Flock } Z = \frac{90}{300} \][/tex]
[tex]\[ \text{Food Percentage for Flock } Z = 0.30 \][/tex]
### Step 2: Calculate the Simulated Number of Birds in Each Flock for the 2nd Generation
Now, we multiply the food percentage for each flock by the total number of birds (30) to find the simulated number of birds in each flock for the 2nd generation.
#### For Flock [tex]\(X\)[/tex]:
[tex]\[ \text{Simulated Number of Birds in Flock } X = \text{Food Percentage for Flock } X \times 30 \][/tex]
[tex]\[ \text{Simulated Number of Birds in Flock } X = 0.19 \times 30 \][/tex]
[tex]\[ \text{Simulated Number of Birds in Flock } X = 5.7 \][/tex]
#### For Flock [tex]\(Y\)[/tex]:
[tex]\[ \text{Simulated Number of Birds in Flock } Y = \text{Food Percentage for Flock } Y \times 30 \][/tex]
[tex]\[ \text{Simulated Number of Birds in Flock } Y = 0.51 \times 30 \][/tex]
[tex]\[ \text{Simulated Number of Birds in Flock } Y = 15.3 \][/tex]
#### For Flock [tex]\(Z\)[/tex]:
[tex]\[ \text{Simulated Number of Birds in Flock } Z = \text{Food Percentage for Flock } Z \times 30 \][/tex]
[tex]\[ \text{Simulated Number of Birds in Flock } Z = 0.30 \times 30 \][/tex]
[tex]\[ \text{Simulated Number of Birds in Flock } Z = 9.0 \][/tex]
### Summary
Let's summarize our results in the table.
\begin{tabular}{|l|l|l|l|}
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & Flock [tex]\(X\)[/tex] & Flock [tex]\(Y\)[/tex] & Flock [tex]\(Z\)[/tex] \\
\hline Total Pieces of Food Eaten & 57 & 153 & 90 \\
\hline Food Percentage & 0.19 & 0.51 & 0.30 \\
\hline Simulated Number of Birds in Flock for 2nd Generation & 5.7 & 15.3 & 9.0 \\
\hline
\end{tabular}
This completes our detailed step-by-step solution for calculating both the food percentages and the simulated number of birds in each flock for the 2nd generation.
