Your school is planning a trip for 226 members. A bus holds 70 people and a van holds 8 people. The bus will cost $280 to rent while the van is only $70. The school has a budget of $980. Write the system of equations to find how many buses and vans should be rented.
Let's assume that x buses and y vans are rented.
Since a bus holds 70 people, the number of people that can be transported by buses is 70x.
Similarly, the number of people that can be transported by vans is 8y.
The total number of people that need to be transported is 226.
So, the first equation is:
70x + 8y = 226
The cost of renting a bus is $280 and the cost of renting a van is $70.
The total budget for the trip is $980.
So, the second equation is:
280x + 70y = 980
Hence, the system of equations is:
\[
\begin{aligned}
70x + 8y &= 226 \\
280x + 70y &= 980 \\
\end{aligned}
\]
Let's denote the number of buses as "b" and the number of vans as "v".
The first equation represents the total number of people that need transportation:
70b + 8v = 226
The second equation represents the cost of renting the vehicles:
280b + 70v = 980
These two equations should help us determine how many buses and vans should be rented.