Sure, let's go through this step-by-step to solve the problem systematically.
### Step 1: Calculate the Food Percentage for Each Flock
We start with the given data:
- Total pieces of food eaten by flock X: 147
- Total pieces of food eaten by flock Y: 93
- Total pieces of food eaten by flock Z: 60
- Total pieces of food eaten overall: 300
To find the food percentage for each flock, we divide the amount of food eaten by each flock by the total food eaten and then multiply by 100 to convert it into a percentage.
#### Flock X:
[tex]\[
\text{Food Percentage for Flock X} = \left( \frac{147}{300} \right) \times 100 = 49\%
\][/tex]
#### Flock Y:
[tex]\[
\text{Food Percentage for Flock Y} = \left( \frac{93}{300} \right) \times 100 = 31\%
\][/tex]
#### Flock Z:
[tex]\[
\text{Food Percentage for Flock Z} = \left( \frac{60}{300} \right) \times 100 = 20\%
\][/tex]
So, the food percentages are:
- Flock X: 49%
- Flock Y: 31%
- Flock Z: 20%
### Step 2: Calculate the Simulated Number of Birds in Each Flock for the 3rd Generation
Given:
- Total number of birds: 30
To find the simulated number of birds in each flock, we multiply the food percentage (in decimal form) by the total number of birds.
#### Flock X:
[tex]\[
\text{Number of Birds in Flock X} = \left( \frac{49}{100} \right) \times 30 = 14.7
\][/tex]
#### Flock Y:
[tex]\[
\text{Number of Birds in Flock Y} = \left( \frac{31}{100} \right) \times 30 = 9.3
\][/tex]
#### Flock Z:
[tex]\[
\text{Number of Birds in Flock Z} = \left( \frac{20}{100} \right) \times 30 = 6.0
\][/tex]
Therefore, the simulated number of birds for the 3rd generation in each flock are:
- Flock X: 14.7 birds
- Flock Y: 9.3 birds
- Flock Z: 6.0 birds
### Final Solution
Let's fill in the provided table with the calculated values:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & \text{Flock X} & \text{Flock Y} & \text{Flock Z} \\
\hline \begin{tabular}{l}
\text{Total Pieces of Food Eaten} \\
(\text{from previous page})
\end{tabular} & 147 & 93 & 60 \\
\hline \text{Food Percentage} & 49\% & 31\% & 20\% \\
\hline \begin{tabular}{l} \text{Simulated Number of Birds} \\ \text{in Flock for 3rd Generation} \end{tabular} & 14.7 & 9.3 & 6.0 \\
\hline
\end{tabular}
\][/tex]
