Question 215006
Let 


v = # of vans
b = # of buses



Since "The transportation will include vans, which can hold 7 students each, and buses which can hold 25 students each" and there are a total of "127 students and 4 teachers" (which add to 127+4=131), this means {{{7v+25b=131}}}. This is our first equation.



Also, we're told that "the school has five more vans than buses" which algebraically means {{{v=b+5}}}



{{{7v+25b=131}}} Start with the first equation.



{{{7(b+5)+25b=131}}} Plug in {{{v=b+5}}}



{{{7b+35+25b=131}}} Distribute.



{{{32b+35=131}}} Combine like terms on the left side.



{{{32b=131-35}}} Subtract {{{35}}} from both sides.



{{{32b=96}}} Combine like terms on the right side.



{{{b=(96)/(32)}}} Divide both sides by {{{32}}} to isolate {{{b}}}.



{{{b=3}}} Reduce.



So 3 buses will be used.



{{{v=b+5}}} Go back to the second equation.



{{{v=3+5}}} Plug in {{{b=3}}}



{{{v=8}}} Add



So 8 vans will be used.