Let's say there are b students per bus and v students per van.
The two equations we have are
[tex]6v + 8b = 202[/tex]
[tex]12v + 10b = 284[/tex]
Doubling the first,
[tex]12v + 16b = 404[/tex]
Subtracting,
[tex]16b - 10 b = 404 - 284[/tex]
[tex]6b = 120[/tex]
[tex]b=20[/tex]
[tex]6v=202 - 8b[/tex]
[tex]v=(202 - 8(20))/6 = 42/6 = 7 [/tex]
Answer: 7 per van, 20 per bus
Check:
[tex]6(7) + 8(20) = 42 + 160 = 202 \quad\checkmark[/tex]
[tex]12(7) + 10(20) = 84 + 200 =284 \quad\checkmark[/tex]
