Question

The 8th graders at Suncrest and Moonvalley planned separate trips to the water park. Suncrest rented and filled 3 vans and 5 buses with 259 students. Moon valley rented and filled 9 vans and 8 buses with 469 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?

Answer 1

A Van can carry 13 students and a bus can carry 44 students.

Explanation:

As given in the question number of students in each bus and each van carried same number of students.

Let the number of students in van be x.

Let the number of students in bus be y.

According to the question the equations will be

`3x + 5y = 259` --------> Eqn. (1)

`9x + 8y = 469` ---------> Eqn. (2)

On multiplying Eqn(1) by 3 and subtracting with Eqn(2) we get

`9x + 15y - (9x+8y) = 777-469\\9x+15y-9x-8y = 308\\7y = 308\\`

`y = 44`

On putting value of y in eq (1) we get

`3x + 5 * 44 = 259`

`3x + 220 = 259 \\3x = 259-220\\3x= 39`

`x=13`

Therefore number of students in van is 13 and bus is 44.