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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.
\begin{tabular}{|r|r|r|}
\hline Grade & Girls & Boys \\
\hline 6 & 9 & 12 \\
\hline 7 & 12 & 18 \\
\hline 8 & 15 & 20 \\
\hline 9 & 25 & 36 \\
\hline
\end{tabular}

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 [tex]$\square$[/tex] and [tex]$\square$[/tex].



Answer :

GinnyAnswer
To determine which two grades have a proportional relationship between the numbers of girls and boys, we need to compare the ratios of girls to boys for each grade.

Let's look at the given data and compute the ratio of girls to boys for each grade:

1. Grade 6
- Girls: 9
- Boys: 12
- Ratio: [tex]\( \frac{9}{12} = \frac{3}{4} \)[/tex] or 0.75

2. Grade 7
- Girls: 12
- Boys: 18
- Ratio: [tex]\( \frac{12}{18} = \frac{2}{3} \)[/tex] or approximately 0.667

3. Grade 8
- Girls: 15
- Boys: 20
- Ratio: [tex]\( \frac{15}{20} = \frac{3}{4} \)[/tex] or 0.75

4. Grade 9
- Girls: 25
- Boys: 36
- Ratio: [tex]\( \frac{25}{36} = \)[/tex] approximately 0.694

Now, we compare the ratios:

- Grade 6: 0.75
- Grade 7: 0.667
- Grade 8: 0.75
- Grade 9: 0.694

We see that Grades 6 and 8 both have the same ratio of 0.75. Therefore, the relationship between the numbers of girls and boys is proportional in Grades 6 and 8.

So, the two grades that have a proportional relationship between the numbers of girls and boys are:

6 and 8