Question

195 students went on a trip. they took 7 vehicles some cars and some buses. find the number of cars and the number of buses they took if each car holds 5 students and each bus hold 45 students.

Explanation:

Step1: Define variables

Let \( x \) be the number of cars and \( y \) be the number of buses. We know that the total number of vehicles is 7, so \( x + y = 7 \). Also, the total number of students is 195, and since each car holds 5 students and each bus holds 45 students, we have the equation \( 5x + 45y = 195 \).

Step2: Solve the system of equations

From the first equation \( x = 7 - y \). Substitute this into the second equation:
\[

$$\begin{align*} 5(7 - y) + 45y &= 195\\ 35 - 5y + 45y &= 195\\ 35 + 40y &= 195\\ 40y &= 195 - 35\\ 40y &= 160\\ y &= \frac{160}{40}\\ y &= 4 \end{align*}$$

\]

Answer:

The number of buses they took is 4.