Question

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 were needed for the trip?

Answer 1

Let x be the number of buses, and y the number of cars.
$\left \{ {{x+y=21} \atop {30x+4y=318}} \right.$
We can solve for y in the first equation to get:
$y=21-x$
Now we can replace 21-x in our second equation, and solve for x:
$30x+4(21-x)=318$
$30x+84-4x=318$
$26x=234$
$x= \frac{234}{26}$
$x=9$

We can conclude that 9 buses were needed for the trip.