Respuesta :
Let V be the number of students that fit inside a van and B the number of students that fit inside a bus. Since 366 students fit in 2 vans and 6 buses, then:
[tex]2V+6B=366[/tex]Since 213 students fit in 6 vans and 3 buses, then:
[tex]6V+3B=213[/tex]Multiply the second equation by 2:
[tex]\begin{gathered} 2(6V+3B)=2(213) \\ \Rightarrow12V+6B=426 \end{gathered}[/tex]Then, we have the system:
[tex]\begin{gathered} 2V+6B=366 \\ 12V+6B=426 \end{gathered}[/tex]Substract the first equation from the second one and solve for V:
[tex]\begin{gathered} (12V+6B)-(2V+6B)=426-366 \\ \Rightarrow12V-2V+6B-6B=60 \\ \Rightarrow10V=60 \\ \Rightarrow V=\frac{60}{10} \\ \therefore V=6 \end{gathered}[/tex]Substitute V=6 into the first equation and solve for B:
[tex]\begin{gathered} 2V+6B=366 \\ \Rightarrow2(6)+6B=366 \\ \Rightarrow12+6B=366 \\ \Rightarrow6B=366-12 \\ \Rightarrow6B=354 \\ \Rightarrow B=\frac{354}{6} \\ \therefore B=59 \end{gathered}[/tex]Therefore, a van has 6 students and a bus has 59 students.
