To solve the problem step by step, we will break down the information given in the question and calculate the required values systematically.
### Step 1: Determine the populations of villages A, B, and C
The total population of the three villages A, B, and C is 80,000, and the ratio of their populations is 5:4:7.
Let the populations of villages A, B, and C be represented as:
- A = 5x
- B = 4x
- C = 7x
The sum of their populations is:
\[ 5x + 4x + 7x = 16x \]
Setting this equal to the total population:
\[ 16x = 80,000 \]
Now, solving for x:
\[ x = \frac{80,000}{16} = 5,000 \]
Now we can find the populations:
- Population of A = \( 5 \times 5,000 = 25,000 \)
- Population of B = \( 4 \times 5,000 = 20,000 \)
- Population of C = \( 7 \times 5,000 = 35,000 \)
### Step 2: Calculate the age distribution in village A
In village A:
- 16% of the population is 61 years or more.
- 36% of the population is between 31 and 61 years.
- The remaining population is less than 31 years.
Calculating the number of villagers in each age group:
- Age 61 or more:
\[ 16\% \text{ of } 25,000 = \frac{16}{100} \times 25,000 = 4,000 \]
- Age between 31 and 61:
\[ 36\% \text{ of } 25,000 = \frac{36}{100} \times 25,000 = 9,000 \]
- Age less than 31:
\[ 25,000 - (4,000 + 9,000) = 25,000 - 13,000 = 12,000 \]
### Step 3: Calculate the age distribution in village B
In village B:
- One-fifth of the population is 61 years or more.
- \( \frac{12}{25} \) of the remaining population is between 31 and 61 years.
Calculating the number of villagers in each age group:
- Age 61 or more:
\[ \frac{1}{5} \text{ of } 20,000 = 4,000 \]
- Remaining population:
\[ 20,000 - 4,000 = 16,000 \]
- Age between 31 and 61:
\[ \frac{12}{25} \text{ of } 16,000 = \frac{12 \times 16,000}{25} = 7,680 \]
- Age less than 31:
\[ 16,000 - 7,680 = 8,320 \]
### Step 4: Calculate the age distribution in village C
In village C:
- The number of villagers aged 61 or more is 50% more than the difference between the number of villagers in A (less than 31 years) and B.
Calculating the difference:
- Difference = \( 12,000 - 8,320 = 3,680 \)
- Villagers aged 61 or more in C:
\[ 3,680 \times 1.5 = 5,520 \]
Now, the number of villagers aged between 31 and 61 in C is 80% more than in A:
- Age between 31 and 61 in A = 9,000
- Age between 31 and 61 in C:
\[ 9,000 \times 1.8 = 16,200 \]
Calculating the remaining population in C:
- Total population of C = 35,000
- Age less than 31:
\[ 35,000 - (5,520 + 16,200) = 35,000 - 21,720 = 13,280 \]
### Step 5: Calculate the male and female populations in village A
The ratio of males to females in village A is 23:27.
Let the number of males be \( 23y \) and females be \( 27y \):
\[ 23y + 27y = 25,000 \]
\[ 50y = 25,000 \]
\[ y = 500 \]
Calculating the number of males and females:
- Males = \( 23 \times 500 = 11,500 \)
- Females = \( 27 \times 500 = 13,500 \)
### Step 6: Calculate the number of females aged 61 or more in village A
From the total population aged 61 or more in village A (4,000), 9/16 are females:
- Females aged 61 or more:
\[ \frac{9}{16} \times 4,000 = 2,250 \]
### Step 7: Calculate the percentage of females aged 61 or more in village A
To find the percentage of females aged 61 or more relative to the total female population:
\[ \text{Percentage} = \left( \frac{2,250}{13,500} \right) \times 100 \]
Calculating:
\[ \text{Percentage} = \left( \frac{2,250}{13,500} \right) \times 100 = \frac{225}{1350} \times 100 = 16.67\% \]
### Final Answer
The percentage of the female population in village A that is equal to 61 years or more is approximately **16.67%**.
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