December 2022

To answer this, we’ll have to set up a system of equations. In the following equations, b represents the number of buses at the start, g represents the number of students in the grade, and n represents the number of students in each bus at the start.

At the beginning, you can find the number of students in each bus by dividing the number of students by the number of buses. This gives you the following equation:
g/b = n
It’s important to note that at any given point you can calculate the amount of students per bus by dividing the number of students at that time by the number of buses at that time. The number of students never changes but the number of buses do.

After the 10 buses ran out of gas, the number of buses decreased by 10 and the amount of students per bus increased by 1. This gives you the following equation:
g/(b-10) = n + 1

After 15 more buses broke down, the number of buses decreased by 15 (not counting the decrease from the 10 buses before) and the number of students per bus increased by 3 (this time taking into account the increase of 1 from before). This gives the following equation:
g/(b-25) = n + 3

Substituting g/b for n (from the first equation) into the last two equations gives the following system of equations:
1) g/(b-10) = g/b + 1
2) g/(b-25) = g/b + 3


Solving the equation 1 for g gives you g = (b^2 - 10b)/10
Substituting this into equation 2 will let you find the value of b, which is 100
Substituting 100 for b in equation 1 will let you find the value of g, which is 900


Therefore, the answer is 900. There were 900 students in the grade that went onto 100 buses, making it so there were 9 students per bus originally. Then 10 of the buses ran out of gas, and 900 students were on 90 buses making it so there were 10 students per bus. Then 15 buses broke down, and 900 students were on 75 buses making it so there were 12 students per bus.