SOLUTION: school a and b go on separate trips, school A rented and filled 6 vans and 5 buses with 208 students. school B rented and filled 12 vans and 4 buses with 224 students. each van and

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: school a and b go on separate trips, school A rented and filled 6 vans and 5 buses with 208 students. school B rented and filled 12 vans and 4 buses with 224 students. each van and      Log On


   

Question 920342: school a and b go on separate trips, school A rented and filled 6 vans and 5 buses with 208 students. school B rented and filled 12 vans and 4 buses with 224 students. each van and each bus carried the same number of students. how many students can a van carry?how many students can a bus carry?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you have 2 equations.

6v + 5b = 208
12v + 4b = 224

you need to solve these equations simultaneosly to get a common solution for v and b.

multiply both sides of the first equation by 2 to get:

12v + 10b = 416
12v + 4b = 224

subtract the second equation from the first to get:

6b = 192

divide this equation by 6 to get:

b = 32

replace b with 32 in the first original equation to get:

6v + 5b = 208 becomes:

6v + 5*32 = 208

solve for v to get:

v = 8

you have v = 8 and b = 32

confirm by replacing v with 8 and b with 32 in both your original equations.

6v + 5b becomes 6*8 + 5*32 which becomes 48 + 160 which becomes 208 which agrees with the first original equation.

12v + 4b becomes 12*8 + 4*32 which becomes 96 + 128 which becomes 224 which agrees with the second original equation.

your solution is confirmed as good.

v = 8
b = 32