To determine which teacher-to-student ratios maintain the proportional relationship described in the table, let's first identify the common ratio from the given data.
The table states:
- For Grade 6: 1 teacher to 25 students
- For Grade 7: 2 teachers to 50 students
- For Grade 8: 3 teachers to 75 students
When simplified, each of these ratios reduces to:
[tex]\[ \frac{25}{1} = 25, \][/tex]
[tex]\[ \frac{50}{2} = 25, \][/tex]
[tex]\[ \frac{75}{3} = 25. \][/tex]
Therefore, the teacher-to-student ratio is consistently 1:25 across grades.
Now, let's examine the new given ratios:
1. For 5 teachers and 125 students:
[tex]\[ \frac{125}{5} = 25. \][/tex]
This is the same as the original ratio of 1:25, so it maintains the proportional relationship.
2. For 4 teachers and 120 students:
[tex]\[ \frac{120}{4} = 30. \][/tex]
This differs from the original ratio of 1:25, so it does not maintain the proportional relationship.
In conclusion:
- The ratio of 5 teachers to 125 students maintains the proportional relationship.
- The ratio of 4 teachers to 120 students does not maintain the proportional relationship.
