Question

The senior classes at High School A and High School B planned separate

trips to the state fair. The senior class at High School A rented and filled 3
vans and 13 buses with 628 students. High School B rented and filled 9
vans and 2 buses with 182 students. Every van had the same number of
students in it as did the buses. Find the number of students in each van
and in each bus. *
Van: 10, Bus: 46
Van: 15, Bus: 70
Van: 4, Bus: 22
Van: 46, Bus: 10

Answer 1

Answer: Van: 10, Bus: 46

Explanation:

Let the number of students in each van be represented by v.

Let the number of students in each bus be represented by b.

The question given can be formed into an equation as:

3v + 13b = 628 ...... i

9v + 2b = 182 ......... ii

Multply equation i by 9

Multiply equation ii by 3

27v + 117b = 5652 ........ iii

27v + 6b = 546 ....... iv

Subtract iv from iii

111b = 5106

b = 5106/111

b = 46

Bus = 46

Recall that 9v + 2b = 182

9v + 2(46) = 182

9v + 92 = 182

9v = 182 - 92

9v = 90

v = 90/9

v = 10

Van = 10