Need help solving system of equations word problems

Question

A class of 285 students went of a field trip. They took 9 vehicles, some cars and some buses. Each car holds 5 students and each bus holds 45 students. Write and solve a system of equations to find the numbers of cars and the number of buses. 

 

Cars=_________           Buses_________    

Answer 1

Let  B= number of Buses

      C = number of cars

 

 

45 students per Bus

  5 students per Car so we can write the equation:   45B + 5C = 285 

                       There is a total of 9 vehicles so:         B +   C = 9

 

to solve linear eqns we can mult one eqn and add or subt to eliminate one variable

so by mult 2ND equation by -5 and adding to the 1st equation we eliminate C and solve for B

 

                                      45B  +  5C = 285

                                      -5B    - 5C = -45

                                      ---------------------

                                      40B   +  0  =  240      So  B = 6   (number of buses)

 

Since  B + C = 9,  so substituting B=6   we get  6 + C = 9  or C = 3 (number of cars)

 

to check:   6 buses with 45 students = 270

                3 cars    with  5 students =   15

               -------------------------------------

                9 vehicles                         285 students