In a school of 2100 students, the ratio of teachers to students is 1:14. Some teachers join the school and the ratio changes to 2:21. Find the number of teachers who joined the school.

Question

Andrea Monroe

Mathematics

4 June, 11:10

In a school of 2100 students, the ratio of teachers to students is 1:14. Some teachers join the school and the ratio changes to 2:21. Find the number of teachers who joined the school.

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Max Hudson · Answer 1

50 Teachers

Step-by-step explanation:

To solve this problem, we first need to find the number of teachers before the new teachers were added. To do so, I created Model 1. On the bottom of the ratios, we have students. On the top, is teachers. The X is the number of teachers we are trying to find. Following the model, I multiplied 2,100 x 1 (2,100) and divided it by 14 to get 150 teachers. Then, I set up a similar model with the new student-teacher ratio (Model 2). From there, I multiplied 2,100 x 2 (4,200) and divided it by 21 to get 200 teachers. Now I have the original number of teachers and the new number of teachers. Subtract the new by the original to find the teachers added and you get the answer of 50 teachers added.