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Math Help - Need assistants with solving a word problem.

  1. #1
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    Need assistants with solving a word problem.

    Parking lot boredom. A parking lot attendant counted 50 vehicles on the lot consisting of four-wheel vehicles, three-wheel vehicles, and two wheel vehicles. She then counted 192 tires touching the ground and observed that the number of four-wheel vehicles was nine times the total of other vehicles on the lot. Use a system of equations and matrices to determine how many of each type of vehicle was on the lot.
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  2. #2
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    Re: Need assistants with solving a word problem.

    Hello, Rich5553!

    A parking lot attendant counted 50 vehicles on the lot consisting of 4-wheel, 3-wheel, and 2-wheel vehicles.
    She counted a total of 192 tires and noted that the number of 4-wheel vehicles was 9 times the total of other vehicles on the lot.
    Use a system of equations and matrices to determine how many of each type of vehicle was on the lot.

    Let: . \begin{Bmatrix}F &=& \text{no. of 4-wheel vehicles} \\ T &=& \text{no. of 3-wheel vehicles} \\ B &=& \text{no. of 2-wheel vehicles} \end{Bmatrix}

    We are given three facts: . \begin{Bmatrix}F + T + B \;=\; 50 \\ 4F + 3T + 2B \;=\; 192 \\ F \;=\; 9(T+B) \end{Bmatrix}

    We have this system of equations: . \begin{Bmatrix} F+T+B &=& 50 \\ 4R + 3T + 2B &=& 192 \\ F - 9T - 9B &=& 0 \end{Bmatrix}

    The matrix is: . \left[\begin{array}{ccc|c} 1&1&1&50 \\ 4&3&2&192 \\ 1&\text{-}9&\text{-}9 & 0 \end{array}\right]

    Go for it!


    You should get \begin{bmatrix}45 \\ 2 \\ 3 \end{bmatrix}

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  3. #3
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    Re: Need assistants with solving a word problem.

    Thank you so much I really need that help.
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