Question

In a traffic sensor installed at a crossing, a check was made on the people carried by 200 cars. This was at a time when most people could be assumed to be driving to work. The result was that:- 96 of cars carried only drivers, 39 carried 2 people, 34 carried 3 people, 22 carried 4 people, 6 carried 5 people.

1. Find the total number of people carried by 200 cars by matrix method.
2. What was the average number of people per car? Comment.
3. What are the values reflected in the question?

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{count}\mathrm{of}\mathrm{cars}\mathrm{carrying}\mathrm{different}\mathrm{number}\mathrm{of}\mathrm{persons}\mathrm{can}\mathrm{be}\mathrm{represented}\mathrm{by}1\times 5\mathrm{matrix}. \\ \mathrm{Let}\mathrm{it}\mathrm{be}\mathrm{denoted}\mathrm{by}\mathrm{A}. \\ \mathrm{Now},\mathrm{A}=\left[\begin{array}{ccccc}96& 39& 34& 22& 6\end{array}\right] \\ \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{persons}\mathrm{sitting}\mathrm{in}\mathrm{the}\mathrm{car}\mathrm{can}\mathrm{be}\mathrm{represented}\mathrm{by}5\times 1\mathrm{matrix}. \\ \mathrm{Let}\mathrm{it}\mathrm{be}\mathrm{denoted}\mathrm{by}\mathrm{B}. \\ \mathrm{Now},\mathrm{B}=\left[\begin{array}{c}1\\ 2\\ 3\\ 4\\ 5\end{array}\right] \\ \mathrm{Now},\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{person}\mathrm{in}\mathrm{all}\mathrm{the}\mathrm{cars}\mathrm{is}\mathrm{given}\mathrm{by}\mathrm{matrix}\mathrm{multiplication}\mathrm{of}\mathrm{AB}. \\ \mathrm{AB}=\left[\begin{array}{ccccc}96& 39& 34& 22& 6\end{array}\right]\left[\begin{array}{c}1\\ 2\\ 3\\ 4\\ 5\end{array}\right]=\left[\begin{array}{c}96\times 1+39\times 2+34\times 3+22\times 4+6\times 5\end{array}\right]=\left[\begin{array}{c}96+78+102+88+30\end{array}\right]=\left[\begin{array}{c}394\end{array}\right] \\ \mathrm{So},\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{persons}=394 \end{gathered}$$

$$\begin{gathered} \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{cars}=197 \\ \mathrm{average}\mathrm{number}\mathrm{of}\mathrm{persons}\mathrm{sitting}\mathrm{in}\mathrm{each}\mathrm{car}=\frac{394}{197}=2 \end{gathered}$$