To find the proportion that gives the number of teachers $t$ needed for 105 students, we start with the given ratio of 2 teachers for every 15 students. We set up a proportion as follows:

$\frac{2}{15} = \frac{t}{105}$

This equation states that the ratio of teachers to students remains the same for both cases.

Solving the Proportion

1. Cross-multiply to solve for $t$: $2 \times 105 = 15 \times t$ $210 = 15t$

2. Divide both sides by 15: $t = \frac{210}{15} = 14$

Therefore, 14 teachers are needed for 105 students.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. What if the school changes the requirement to 3 teachers for every 20 students? How many teachers would be needed for 140 students?
2. If a school has 10 teachers, how many students can they accommodate under the original ratio?
3. How would the proportion change if the number of teachers required increases to 5 for every 15 students?
4. If there are 70 students, how many teachers are needed using the original proportion?
5. Can you solve for the number of students if a school hires 8 teachers under the original ratio?

Tip: When setting up proportions, always ensure the units match on both sides of the equation (e.g., teachers with teachers, students with students).