system of equations word problems

Question

All 231 students in the Math Club went on a field trip. Some students rode in vans which hold 7 students each and some students rode in buses which hold 25 students each. How many of each type of vehicle did they use if there were 15 vehicles total?

Answer 1

They used 7 buses and 8 vans.

Lets take no. of bus = x and no. of vans = y

Firstly form the equations :

1) x + y = 15

2) 25x + 7y = 231

Take the first equation ⇒ x + y = 15 ⇒ y = 15 - x

now place the value y = 15- x into the second equation:

25x +7(15-x) = 231

25x +105-7x = 231

25x-7x+105=231

18x=231-105

18x=126

x=7

Now place the value x=7 into ⇒ y= 15-x ⇒ y=15-7 ⇒ y = 8

Answer 2

V+B = 15

7V+25B = 231

7V +7B =105 subtract

18B = 126

B = 7 buses

V= 8 vans

7(8)+25(7) = 56 + 175 = 231

7+8 = 15