What is the average number of villagers in Village B, D, E, and F together?
Understand the Problem
The question is asking for the average number of villagers in villages B, D, E, and F combined. We need to determine the populations of these villages based on the given percentages of the total population of City 'X' and then calculate the average.
Answer
The average number of villagers in villages B, D, E, and F combined is \( 14400 \).
Answer for screen readers
The average number of villagers in villages B, D, E, and F combined is ( 14400 ).
Steps to Solve
- Determine the total population of City X
Let the total population of City X be ( P ).
- Calculate the populations of each village
- Population of Village A: ( 0.25P )
- Population of Village B: ( 0.20P )
- Population of Village C: ( \frac{2}{5}P = 0.4P )
- Population of Village D: ( 0.60 \times \text{Population of Village C} = 0.60 \times 0.4P = 0.24P )
- Population of Village E: ( 0.85 \times \text{Population of Village B} = 0.85 \times 0.20P = 0.17P )
- Population of Village F: Given that the total population of Village F is 21000, with 35% of the total population: [ 0.35P = 21000 \implies P = \frac{21000}{0.35} = 60000 ]
- Compute the populations of villages B, D, E, and F
- Village B: ( 0.20 \times 60000 = 12000 )
- Village D: ( 0.24 \times 60000 = 14400 )
- Village E: ( 0.17 \times 60000 = 10200 )
- Village F: Given as ( 21000 )
- Find the total population of villages B, D, E, and F combined
Combine the populations: [ 12000 + 14400 + 10200 + 21000 = 57600 ]
- Calculate the average population of villages B, D, E, and F
The number of villages is 4: [ \text{Average} = \frac{57600}{4} = 14400 ]
The average number of villagers in villages B, D, E, and F combined is ( 14400 ).
More Information
This problem involves calculating percentages and understanding the relationships between different parts of a whole. By finding the total population and the specific percentages allocated to each village, we derived the average population effectively.
Tips
- Incorrectly adding percentages together without converting them into actual numbers.
- Forgetting to convert back into the total population after using percentages.
- Not dividing the total by 4 when calculating the average.
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