Number of students per van = v
Number of students per bus = b
Equation 1: 7v + 10b = 332
Equation 2: 4v + 15b = 459
Solving for b equation 1:
7v + 10b = 332 ==> 10b = 332 - 7v ==> b = (332 - 7v)/10
Using this value into equation 2:
4v + 15b = 459 ==> 4v + 15(332 - 7v)/10 = 459 ==> 40v + 15(332 - 7v) = 4590
40v + 4980 - 105v = 4590 ==> -65v = 4590 - 4980 = -390
v = 390/65 = 6
v = 6
Using this value in the expression we found for b:
b = (332 - 7v)/10 = (332 - 7*6)/10 = (332 - 42)/10 = 290/10 = 29
b = 29
Answer:
Students in each van = 6
Students in each bus = 29