Number of vehicles needed for field trip

Question

Field trip for 142 students and 6 drivers.  Buses hold 51 passengers and vans hold 10 passengers.  Write a system of equations to find out how many buses and vans will be needed.

Answer 1

Let x=the number of buses

Let y=the number of vans

 

    x+y=6  This equation is based upon the total number of vehicles would be driven being equal to 6 drivers.

51x+10y=142 This equation is based upon the total number of students riding on x number of buses and y number of vans.

 

For this particular problem, I like to use elimination of a variable and solve for the other, then substitute it into one of the original equation to solve for the other variable. Multiply the first equation by -10 to eliminate the variable y.

 

-10x-10y=-60

  51x+10y=142  Add the two equations.

 

41x=82 Divide both sides by 41

    x=2 Substitute this into the first equation.

 2+y=6

-2     -2

 

      y=4

 

Therefore, 2 buses and 4 vans would be needed for this field trip.