To determine the correct answer, we first need to find the student-to-teacher ratio given in the problem.

Step 1: Calculate the Initial Ratio

The school has:

• 1,360 students
• 80 teachers

So, the ratio of students to teachers is: $\frac{1360}{80} = 17 \text{ students per teacher}$

Step 2: Identify Equivalent Ratios

Now, let's check each of the provided options to see which match this ratio.

1. 170 students to 10 teachers
   $\frac{170}{10} = 17$ — This matches the original ratio.

2. 2 students to 34 teachers
   $\frac{2}{34} = \frac{1}{17} \neq 17$ — This does not match.

3. 34 students to 2 teachers
   $\frac{34}{2} = 17$ — This matches the original ratio.

4. 10 students to 170 teachers
   $\frac{10}{170} = \frac{1}{17} \neq 17$ — This does not match.

Conclusion

The two ratios that are equivalent to the original are:

• 170 students to 10 teachers
• 34 students to 2 teachers

Would you like further details or have any questions?

Related Questions

1. How do you simplify ratios in general?
2. Why is it important to compare ratios in real-world scenarios?
3. How can ratios be applied in classroom settings beyond student-teacher ratios?
4. What are some other practical examples where ratios are commonly used?
5. How do you convert a ratio into a fraction or percentage?

Tip

When simplifying ratios, divide both terms by their greatest common divisor (GCD) to get the simplest form.