Answer:
8 students per van and 46 students per bus
Step-by-step explanation:
Let the number of people in each van be v.
Let the number of people in each bus be b.
High School A:
1 van and 6 buses, 284 students
1 van had 1 * v people, or simply v students.
6 buses had 6b students.
Total of 284 students.
The first equation is
6b + v = 284
Now we do the same for High School B.
1 van and 5 buses, 238 students
1 van had v students
5 buses had 5b students
Total of 238 students.
The second equation is
5b + v = 238
We have 2 equations in 2 unknowns.
6b + v = 284
5b + v = 238
Rewrite the first equation. Multiply both sides of the second equation by -1 and write it below the first equation. Then add the equations.
6b + v = 284
(+) -5b - v = -238
----------------------------
b = 46
The number of students per bus is 46.
Now we use the first equation, substitute 46 for b, and solve for v.
6b + v = 284
6(46) + v = 284
276 + v = 284
v = 8
The number of students per van is 8.
Answer: 8 students per van and 46 students per bus
