The seniors and juniors at Sweet Valley High School are going on a trip to Busch Gardens. The seniors filled 12 vans and 12 buses with 564 total students. The juniors
filled 6 vans and 13 buses with 492 students. How many students were in each van? In
each bus?

Solve the system of equations

buses can hold 30 and vans can hold 17.

Step-by-step explanation:

Let the amount a van can hold be v and the amount a bus can hold be b.

12 vans and 12 buses totals 564: 12v + 12b = 564 (equation 1)

6 vans and 13 buses totals 492: 6v + 13b = 492 (equation 2)

Subtract 2 times equation 2 from equation1, we get 14b = 420.

Thus, b = 30.

Since 12v + 12b = 564, plugging in b=30, 12v + (12)(30) = 564, so v = 17.

x = 12

y = 15

step-by-step explanation: