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2 July, 08:37

The county fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 11 vans and 9 buses with 624 students. High School B rented and filled 5 vans and 1 bus with 126 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.

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  1. 2 July, 11:32
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    Van can carry 15 and bus 51 students

    Explanation:

    Let's mark the number of vans with x and number of buses with y.

    That allows us to write equations:

    1) 11x + 9y = 624 (high school A)

    2) 5x + y = 126 (high school B)

    This means that we have a system of the equations with two unknowns.

    We can use x or y to solve this. Let's use x, but first we need to express y through x. We said that:

    5x + y = 126

    That means that:

    y = 126 - 5x

    Now, let's plug this in the equation 1):

    11x + 9 (126 - 5x) = 624

    11x + 1134 - 45x = 624

    -34x = - 510

    34x = 510

    x = 15

    So, if x is 15, let's plug it in any of the two equations:

    5x + y = 126

    75 + y = 126

    y = 51

    So, a van carry 15 and a bus 51 students.
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