Alright, let's go through the problem step-by-step to find the percentage of the class that is female.
1. Given Information:
- There are 32 female students in the class.
- The ratio of female students to male students is 16:9.
2. Understanding the Ratio:
- The ratio 16:9 translates to:
- For every 16 female students, there are 9 male students.
3. Setting Up the Variables:
- Let the number of male students be [tex]\( m \)[/tex].
- According to the ratio, the number of female students is given by [tex]\( \frac{16}{9} \times m \)[/tex].
4. Total Number of Students:
- The total number of students in the class is the sum of female and male students:
[tex]\[
32 + m
\][/tex]
5. Solving the Ratio Equation:
- Set up the proportion based on the given ratio:
[tex]\[
\frac{32}{32 + m} = \frac{16}{25}
\][/tex]
- Cross-multiply to solve for [tex]\( m \)[/tex]:
[tex]\[
32 \times 25 = 16 \times (32 + m)
\][/tex]
[tex]\[
800 = 512 + 16m
\][/tex]
[tex]\[
800 - 512 = 16m
\][/tex]
[tex]\[
288 = 16m
\][/tex]
[tex]\[
m = \frac{288}{16} = 18
\][/tex]
6. Total Number of Students in the Class:
- Now we can find the total number of students:
[tex]\[
32 + 18 = 50
\][/tex]
7. Calculating the Percentage of Female Students:
- To find the percentage of the class that is female, use the formula:
[tex]\[
\text{Percentage} = \left(\frac{\text{Number of Female Students}}{\text{Total Number of Students}}\right) \times 100
\][/tex]
[tex]\[
\text{Percentage} = \left(\frac{32}{50}\right) \times 100 = 64\%
\][/tex]
8. Conclusion:
- The percentage of the class that is female is:
[tex]\[
\boxed{64\%}
\][/tex]
So, the correct answer is:
d. 64%
