SOLUTION: A group of students are going on a field trip. The transportation will include vans, which can hold 7 students each, and buses which can hold 25 students each the school has five m

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: A group of students are going on a field trip. The transportation will include vans, which can hold 7 students each, and buses which can hold 25 students each the school has five m      Log On


   

Question 215006: A group of students are going on a field trip. The transportation will include vans, which can hold 7 students each, and buses which can hold 25 students each the school has five more vans than buses. If 127 students and 4 teachers are going on the trip, how many vans and buses will be used?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%2B25b=131. This is our first equation.


Also, we're told that "the school has five more vans than buses" which algebraically means v=b%2B5


7v%2B25b=131 Start with the first equation.


7%28b%2B5%29%2B25b=131 Plug in v=b%2B5


7b%2B35%2B25b=131 Distribute.


32b%2B35=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=%2896%29%2F%2832%29 Divide both sides by 32 to isolate b.


b=3 Reduce.


So 3 buses will be used.


v=b%2B5 Go back to the second equation.


v=3%2B5 Plug in b=3


v=8 Add


So 8 vans will be used.