Question

12) Yellowstone National Park is a popular field trip destination. This year the senior class at High School and the senior class at High School B both planned trips there. The senior class at High School A rented and filled with 332 students. of students.High School B rented and filled 4 vans and 15 buses with 459 students. each van and each bus carried the same number of students. find the number of students in each van and in each bus

Answer 1

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