A school is planning a field trip for 142 people. The trip will use 6 drivers and two types of vehicles:buses and vans. A bus can seat 51 passengers. A van can seat 10 passengers. Write and solve a system of equations to find how many buses and vans will be needed
so 51+51=102 and then 10+10+10+10=40, and 102+40=142. So they will need to take 2 buses and 4 vans.
hope I helped
Answer: The answer is 2 buses and 4 vans.
Step-by-step explanation: Let 'b' be the number of buses and 'v' be the number of vans that will be needed.
The trip will use 6 drivers, and we need one driver for each vehicle, so number of drivers is equal to the number of vehicles used.i.e.,
\(b+v=6.\)
Now, number of passengers in buses is 51b and number of passengers in vans is 10v. Since there are total 142 people, so
\(51b+10v=142.\)
Substituting the value of 'v' from forst equation in the second equation, we have
\(51b+10(6-b)=142\\\\\Rightarrow 51b+60-10b=142\\\\\Rightarrow 41b=82\\\\\Rightarrow b=2.\)
Again, from the first equation, we get
\(v=6-2=4.\)
Thus, there are 2 buses and 4 vans in the trip.