To analyze the given ratio of girls to total students, which is 6:11, we can start by determining the implications of this ratio.
Let’s denote:
- G = number of girls
- B = number of boys
- T = total number of students (G + B)
From the ratio G:T = 6:11, we can express it as:
G/T = 6/11 => G = (6/11)T
Since T = G + B, we can also write:
B = T - G = T - (6/11)T = (5/11)T
So now we have:
- Number of girls (G) = (6/11)T
- Number of boys (B) = (5/11)T
Now let's analyze the statements:
A. The ratio of boys to girls is 11:6.
- Since the ratio of girls to boys is 6:5, the ratio of boys to girls is the reciprocal, which would be 5:6, not 11:6. Hence, A is incorrect.
B. The ratio of total students to boys is 11:5.
- The total number of students (T) to boys (B) ratio can be calculated: T:B = T:(5/11)T = 11:5. So, B is correct.
C. A class with 33 students will have 18 girls.
- For 33 students: G = (6/11) * 33 = 18 (correct). Number of boys = (5/11) * 33 = 15. So, C is correct.
D. A class with 34 students will have 22 boys.
- For 34 students: G = (6/11) * 34 = 18.55 (not an integer), which means we cannot have 34 students maintaining the same ratio. Hence, D is incorrect.
E. There is 1 more boy than girl in each class.
- This is false because, from our calculations, for every 6 girls there are 5 boys, meaning that there are actually more girls than boys (6 girls vs. 5 boys). Hence, E is incorrect.
Correct statements: B and C.
3 answers