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23 August, 20:20

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).

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  1. 23 August, 20:21
    0
    Answer: (18,58)
  2. 23 August, 20:33
    0
    The number of students in each van = 18The number of students in each bus = 58 (x, y) = (18,58)

    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
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