all 231 students in the Math club went on a field trip. Some student rode in vans which hold 7 students 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?

7 buses

8 vans

Step-by-step explanation:

We know that out of 231 students, some student rode in vans which hold 7 students and some students rode in buses which hold 25 students each so we can write an equation:

7V + 25B = 231 - - - (1)

And since there were 15 vehicles in total:

V + B = 15 - - - (2)

V = 15 - B

Substituting the value of V in (1):

7 (15-B) + 25B = 231

105 - 7B + 25B = 231

18B = 126

B = 7

Substituting this value of B in (2):

V + 7 = 15

V = 8

8 Vans & 7 buses.

Step-by-step explanation:

Given:

Total number of students = 231

1 van rode = 7 students

1 bus rode = 25 students

Let x denote the number of vans used & y denote the number of bus used, then,

x+y = 15 ... (1)

and, 7x + 25y = 231 ... (2)

On solving eq (1) & (2) we get,

From equation (1), x = 15-y

Putting in eq (2), we get,

7 (15-y) + 25y = 231

105 - 7y + 25y = 231

18y = 126

y = 7

and, x = 15 - 7 = 8

Hence, 8 vans were used & 7 buses were used.