Question

Enrollment at Roosevelt Middle School is being reviewed by the school staff. The table gives the numbers of boys and girls in grades 6 to 9.
Grade Girls Boys
6 9 12
7 12 18
8 15 20
9 25 36

In which two grades is the relationship between the numbers of girls and boys proportional?

The two grades that have a proportional relationship between the numbers of girls and boys are and .
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Answer 1

Answer:

The ratio of the number of boys to the number of girls in the 6th grade and 8th grade are proportional .

Step-by-step explanation:

As given

Enrollment at Roosevelt Middle School is being reviewed by the school staff.

As the table shown in the question.

Ratio of the numbers of girls and boys of 6th grade .

$\frac{Number\ of\ girls}{Number\ of\ boys} = \frac{9}{12}$

Simplify the above

$\frac{Number\ of\ girls}{Number\ of\ boys} = \frac{3}{4}$

Ratio of the numbers of girls and boys of 7th grade .

$\frac{Number\ of\ girls}{Number\ of\ boys} = \frac{12}{18}$

Simplify the above

$\frac{Number\ of\ girls}{Number\ of\ boys} = \frac{2}{3}$

Ratio of the numbers of girls and boys of 8th grade .

$\frac{Number\ of\ girls}{Number\ of\ boys} = \frac{15}{20}$

Simplify the above

$\frac{Number\ of\ girls}{Number\ of\ boys} = \frac{3}{4}$

Ratio of the numbers of girls and boys of 9th grade .

$\frac{Number\ of\ girls}{Number\ of\ boys} = \frac{25}{36}$

Clearly as shown above the ratio of the number of boys to the number of girls in the 6th grade and 8th grade are proportional .

Answer 2

6th grade : 9/12 = 3/4
7th grade : 12/18 = 2/3
8th grade : 15/20 = 3/4
9th grade : 25/36

proportional grades are in 6th and 8th