Chapter 6.2, Problem 24PPE

To determine

the number of buses and vans are required to accommodate the 142 people.

Answer to Problem 24PPE

The number of buses and number of vans are 2, 4.

Explanation of Solution

Given info:

The school field trip is planned for 142 people.

Consider the total number of people is $c=142$

Consider the number of passengers accommodated in bus alone is $a=51$

Consider the number of passengers accommodated in van alone is $b=10$

The trip uses the 6 drivers and 2 vehicles.

Formula used:

Show the standard form for linear equations in two variables is  $Ax+By=C$

Here $A$ is a positive integer, $B$ and $C$ are integers, $x$ is the number of bus and $y$ is the number of van.

Calculation:

Find the number of vehicles by linear equations as follows:

  $\begin{array}{l}x+y=6\\ y=6-x\end{array}$

Find the number of passengers by linear equations as follows:

  $51x+10y=142$

Solve the above equation to find the number of vehicles as follows:

  $\begin{array}{l}51x+10y=142\\ 51x+10\left(6-x\right)=142\\ 51x+60-10x=142\\ 51x-10x=142-60\end{array}$

  $\begin{array}{l}41x=82\\ x=\frac{82}{41}\\ x=2\end{array}$

Find the number of vans $y$ by linear equation as follows:

  $\begin{array}{l}x+y=6\\ y=6-x\\ y=6-2\\ y=4\end{array}$

Hence, the number of buses and number of vans are 2, 4.

Conclusion:

Thus, the number of buses and number of vans are 2, 4.