How do you solve this Linear Algebra Problem?

Use what you know about linear algebra and matrices to solve the following word problem: A rental

company has a

eet of 12 vans which can carry a total of 220 passengers. The vans come in three sizes

(A, B, and C) according to the number of passengers they can hold: 10, 15 and 20, respectively. How

many of each van must be rented so as to carry a total of 220 people? List all possible solutions.

LIN Unit 1 Test Page 2 of

2 Answers

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  • ?
    Lv 4
    1 decade ago
    Favorite Answer

    From this information I can only get 2 appropriate equations:

    a + b + c = 12

    10a + 15b + 20c = 220

    If you were to make it a matrix:

    [ 1 1 1] = [12]

    [ 10 15 20] = [220]

    It's not a square matrix so there is no actual solution

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  • nle
    Lv 7
    1 decade ago

    You have the matrix

    [1 1 1 12 ]

    [10 15 20 220]

    or

    [ 1 1 1 12]

    [ 0 5 10 100 ]

    after using GAUSS elimination

    that means 5B +10C = 100

    or B +2C = 20

    let C= Z (an integer)

    then B = 20 -2Z

    and A = Z - 8

    since A >0 then Z> 8

    since B > 0 then Z <10

    Z > 8 and Z <10 then Z must be 9

    then C = 9 , A = 1 , B = 2

    check :

    A+ B +C =9 +1 + 2 =12

    and 10A + 15B + 20C = 10 + 15(2) +20(9)

    = 10+30 +180 = 220

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