Answer:
Let's break down the problem step by step. Initially, the bus starts with R occupants, including the driver. After each of the 20 stops, 3 people get on the bus, and no one leaves.
To find the number of occupants at the end of the 20th stop, we need to consider the number of people who boarded the bus at each stop. Since 3 people get on the bus at every stop, the total number of people who boarded the bus after all 20 stops is 20 * 3 = 60.
Now, let's look at the information given. It states that the number of occupants at the end of the 20th stop is three times the number of occupants at the end of the 4th stop. Let's denote the number of occupants at the 4th stop as N.
According to the information, the number of occupants at the end of the 20th stop is 3 * N. So we can write the equation:
3 * N = R + 60
We need to find the number of occupants immediately after the 10th stop. Let's denote it as M. Since 10 stops have been completed, the number of occupants at the end of the 10th stop is R + (10 * 3).
To solve for M, we can set up a relationship between the occupants at the end of the 10th stop and the occupants at the end of the 4th stop:
R + (10 * 3) = N
Now, we have two equations:
3 * N = R + 60
R + 30 = N
We can use these equations to solve for N and R. Let's solve for R first:
R + 30 = N
Substituting N in terms of R from the first equation:
R + 30 = (R + 60) / 3
Simplifying the equation:
3R + 90 = R + 60
2R = -30
R = -15
Since we cannot have a negative number of occupants, we can conclude that there was an error in the problem statement or setup. Please verify the given information, as it is not possible to have a negative number of occupants on the bus initially.