Question

I want to know about a specific problem in my homework, that has to do with proportions and ratios, regarding the relationship between the number of students and the number of tables in an art classroom, where 8 students can sit around 1 table, and 48 students can sit around 6 tables, what is the relationship?

Answer 1

To understand the relationship between the number of students and the number of tables in your art classroom problem, let's analyze the information given:

1. You mentioned that 8 students can sit around 1 table. This implies a ratio of students to tables:
\[
\text{Ratio (Students: Tables)} = 8:1
\]

2. You also stated that 48 students can sit around 6 tables. Therefore, we can calculate the number of students per table in this scenario as follows:
\[
\text{Students per table} = \frac{48 \text{ students}}{6 \text{ tables}} = 8 \text{ students/table}
\]

From both situations, we can see that the ratio of students to tables remains consistent at 8 students per table. Therefore, the relationship between the number of students \( S \) and the number of tables \( T \) can be expressed with the equation:

\[
S = 8T
\]

This means for every table, there can be 8 students.

In conclusion, the relationship is linear and can be understood as a consistent ratio of 8 students for each table available in the art classroom. Thus, if you know how many tables there are, you can easily find out how many students can be accommodated by multiplying the number of tables by 8.