Question

all 286 students in the Math Club went on a field trip. Some students rode in vans which hold 11 student each and some students rode in buses which hold 55 students each. How many of each type of vehicle did they use of there were 10 vehicle total?

Answer 1

Answer: 4 buses & 6 vans

Step-by-step explanation:

You have 4 buses so you would multiply 4 by 55 because each bus holds 55 students. Since you have 4 buses, you would have 6 vans because there is a total of 10 vehicles. Therefore, you would also multiply 6 by 11 because each van holds 11 students.

286 (students) = (6 x 11) + (4 x 55)

286 = 66 + 220

Answer 2

Answer: 6 vans and 4 buses were used.

Step-by-step explanation:

Let x represent the number of vans that the students used.

Let y represent the number of buses that the students used.

Some students rode in vans which hold 11 student each and some students rode in buses which hold 55 students each. Since the total number of students in the Math Club that went on a field trip is 286, it means that

11x + 55y = 286 - - - - - - - - - - -1

The total number of vehicles that they used is 10. It means that

x + y = 10

Substituting x = 10 - y into equation 1, it becomes

11(10 - y) + 55y = 286

110 - 11y + 55y = 286

- 11y + 55y = 286 - 110

44y = 176

y = 176/44

y = 4

x = 10 - y = 10 - 4

x = 6