A class of 195 students went on a field trip. They took 19 Vehicles, some cars, some buses .If each can holds 5 students and each bus holds 25 students, how many buses did they take?

Answer 1

Let \( c \) represent the number of cars and \( b \) represent the number of buses. We know from the problem that:

1. The total number of vehicles is 19: \[ c + b = 19 \]
2. Each car holds 5 students and each bus holds 25 students. The total number of students transported is 195: \[ 5c + 25b = 195 \]

Now, we can solve these equations step by step.

First, let's simplify the second equation by dividing everything by 5: \[ c + 5b = 39 \]

We now have the system of equations:

1. \( c + b = 19 \) (1)
2. \( c + 5b = 39 \) (2)

Next, we can use equation (1) to express \( c \) in terms of \( b \): \[ c = 19 - b \]

Now substitute this expression for \( c \) into equation (2): \[ (19 - b) + 5b = 39 \] This simplifies to: \[ 19 + 4b = 39 \] Subtract 19 from both sides: \[ 4b = 20 \] Now divide by 4: \[ b = 5 \]

Now that we have \( b \), we can find \( c \): \[ c = 19 - b = 19 - 5 = 14 \]

Thus, the class took 5 buses.