Sophia’s school took a field trip. a total of 21 vehicles were needed for the trip. some students took the bus, and some students car-pooled. there were 30 people on each bus and 4 people in each car. 318 people altogether attended the trip. how many buses and cars were needed for the trip? can someone me find the x and the y using systems of equations?

We know there were 21 vehicles so one of the equations is:

c+b=21

We can find  the second equation with the other given information:

30b+4c=318

We can use manipulate the first equation then use substitution to solve the system:

c=21-b

We can plug this into the second equation:

30b+4(21-b)=318
30b+84-4b=318
26b+84=318
26b=234
b=9

Now we can plug this into one of the original equations to solve for c (the first equation is easier):

c+9=21
c=12

You can check your work by plugging the answers into the two equations:

12+9=21
21=21

(30)(9)+(4)(12)=318
270+48=318
318=318

There are 9 buses and 12 cars.