Need assistants with solving a word problem.

**Rich5553** · November 8th 2012, 06:52 AM

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.

**Soroban** · November 8th 2012, 09:18 AM

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 $\begin{bmatrix}45 \\ 2 \\ 3 \end{bmatrix}$

**Rich5553** · November 8th 2012, 10:29 AM

Thank you so much I really need that help.

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