8. for the senior class trip the 372 students rented 1 van and 6 buses. at another school the 780 seniors…

8. for the senior class trip the 372 students rented 1 van and 6 buses. at another school the 780 seniors rented 4 vans and 12 buses. every van carried the same number of students and every bus carried the same number of students how many students were in each van and in each bus?

8. for the senior class trip the 372 students rented 1 van and 6 buses. at another school the 780 seniors rented 4 vans and 12 buses. every van carried the same number of students and every bus carried the same number of students how many students were in each van and in each bus?

Answer

Explanation:

Step1: Set up equations

Let (x) be the number of students in a van and (y) be the number of students in a bus. For the first school: (x + 6y=372), so (x = 372 - 6y). For the second school: (4x+12y = 780).

Step2: Substitute (x) into the second equation

Substitute (x = 372 - 6y) into (4x+12y = 780). [ \begin{align*} 4(372-6y)+12y&=780\ 1488-24y + 12y&=780\ 1488-12y&=780\ -12y&=780 - 1488\ -12y&=-708\ y&=59 \end{align*} ]

Step3: Find (x)

Substitute (y = 59) into (x = 372 - 6y). [ \begin{align*} x&=372-6\times59\ x&=372 - 354\ x&=18 \end{align*} ]

Answer:

There are (18) students in each van and (59) students in each bus.