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).

Step-by-step 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

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1