Question

The ski mountain is a popular winter holiday vacation spot. This year the students at university and students at university both planned trips there. The students at university A rented and filled 16 vans and 8 buses and 752 students. The students at university B rented and filled 5 vans and 5 buses with 380 students. Each van and each bus carried the same number of students. Use elimination to solve the system of linear equations and determine how many students a van can carry, x and how many students a bus can carry, y. Write your answer as an ordered pair (x,y).

Answer 1

Answer: (18,58)

Explanation:

Answer 2

The number of students in each van = 18

The number of students in each bus = 58

(x,y) = (18,58)

Explanation:

Let us assume the the number of students a van can carry = x

Let us assume the the number of students a bus can carry = y

At university A:

Total number of students = 752

Total number of vans = 16

So, total students carried by 16 vans = 16 x

The total number of buses = 8

So, total students carried by 8 buses = 8 y

⇒ 16 x + 8 y = 752

or, 2 x + y = 94 ... (1)

At university B:

Total number of students = 380

Total number of vans = 5

So, total students carried by 5 vans = 5 x

The total number of buses = 5

So, total students carried by 5 buses = 5 y

⇒ 5 x + 5 y = 380

or, x + y = 76 .... ... (2)

Now, solving (1) and (2) , we get:

2 x + y = 94

x + y = 76

(-) (- ) (-) ⇒ 2 x - x + y - y = 94 - 76

or, x = 18

Substituting in (2) , we get: y = 76 - 18 = 58 , or y = 58

So, the number of students in each van = 18

The number of students in each bus = 58

(x,y) = (18,58) is the ordered pair