To find the number of men, women, boys, and girls on the island, we need to calculate each category step-by-step using the information provided.
1. Calculate the number of men:
- Given that [tex]\(\frac{2}{5}\)[/tex] of the people are men,
- Total number of people on the island = 480,
- Number of men can be calculated as:
[tex]\[
\text{Number of men} = \frac{2}{5} \times 480
\][/tex]
[tex]\[
\text{Number of men} = 192
\][/tex]
2. Calculate the number of women:
- Given that [tex]\(\frac{1}{3}\)[/tex] of the people are women,
- Total number of people on the island = 480,
- Number of women can be calculated as:
[tex]\[
\text{Number of women} = \frac{1}{3} \times 480
\][/tex]
[tex]\[
\text{Number of women} = 160
\][/tex]
3. Calculate the number of boys:
- Given that [tex]\(\frac{1}{10}\)[/tex] of the people are boys,
- Total number of people on the island = 480,
- Number of boys can be calculated as:
[tex]\[
\text{Number of boys} = \frac{1}{10} \times 480
\][/tex]
[tex]\[
\text{Number of boys} = 48
\][/tex]
4. Calculate the number of girls:
- The total number of people minus the sum of men, women, and boys will give the number of girls,
- Total people = 480,
- Number of men = 192,
- Number of women = 160,
- Number of boys = 48,
- Number of girls can be calculated as:
[tex]\[
\text{Number of girls} = 480 - (192 + 160 + 48)
\][/tex]
[tex]\[
\text{Number of girls} = 480 - 400
\][/tex]
[tex]\[
\text{Number of girls} = 80
\][/tex]
So, the number of people in each category is:
- Men: 192,
- Women: 160,
- Boys: 48,
- Girls: 80.
