Question

There are 120 students in Year 11 at a school.

Each student studies one language, either French, Spanish, German or Welsh.
21 of the 40 students studying Welsh are male.
18 males and 9 females study French.
12 of the 17 students studying Spanish are female.
Twice as many females study German than males.
How many students in Year 11 are female?

Answer 1

By analyzing the distribution of students in language classes and their gender ratios, we find that there are 64 female students in Year 11.

Step-by-step explanation:

The task is to find out how many female students are in Year 11, given the distribution of students among four language classes with known gender ratios. First, we determine the number of males and females in each class from the information provided and then sum up the number of female students.

1. For Welsh: 21 out of 40 students are male, hence 40 - 21 = 19 are female.
2. For French: There are 18 males and 9 females.
3. For Spanish: 12 out of 17 students are female, so 17 - 12 = 5 are male.
4. For German: Let the number of males be x. Therefore, the number of females is 2x. As all students study one language, the sum of students in all four languages classes must equal 120. This gives us the equation 21 + 18 + 5 + x + 19 + 9 + 12 + 2x = 120, which simplifies to 3x + 84 = 120, hence x = 12. Thus, there are 24 females studying German.

Now, we add up the number of female students from all classes: 19 (Welsh) + 9 (French) + 12 (Spanish) + 24 (German) = 64 female students in Year 11.

Answer 2

80 students are female

Step-by-step explanation:

21 are male meaning 19 are female

9 are female in French

12 are female in Spanish

total = 40

2x + 40 = 120

2x = 80

x = 40

females' = 80

total = 80