SOLUTION: The state fair is a popular field trip destination. This year the senior classes at Berkner High School and Richardson High School both planned trips to the fair. Berkner filled 10

From the condition, you get these two equations


10*V + 7*B = 341    students     (1)    (V = is the van capacity;  B = the bus capacity)
 5V  + 8*B = 319    students     (2)


Multiply eq(2) by 2  (both sides).  Keep eq(1) as is. You will get an EQUIVALENT system


10*V +  7*B = 341                (1')  
10V  + 16*B = 638                (2')


Now subtract eq(1') from eq(2').  The terms  "10V" will cancel each other, and you will get a single equation for one unknown  B:


16B - 7B = 638 - 341

9B       = 297           =============>  B = 297/9 = 33.


Now from eq(1),  V =  = 11.


Answer.  The bus capacity is 33 students.  The van capacity is 11 students.