Question

Each 6th grade classroom has the same ratio of girls to boys. The ratio of girls to total students is 6:11.
Select ALL of the statements that are correct.
A.

The ratio of boys to girls is 11:6.
B.

The ratio of total students to boys is 11:5.
C.

A class with 33 students will have 18 girls.
D.

A class with 34 students will have 22 boys.
E.

There is 1 more boy than girl in each class.

Answer 1

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.