Chapter 3.2, Problem 21PPSE

Solution

To find: How many of each type of vehicle could transport all 31 people to the ski area in one trip.

The number of van are 3 and number of sedan are 2.

Given information:

It is given that there are 26 members in a group and five chaperons. The number of seat in van is7 and number of seats in sedan are five.

Concept used: Substitution. Method of solving system of linear equation

Calculation:

Let the number of van be $x$ and number of sedan be $y$ .

There are 5 chaperons who drive either van or sedan that means total number of vehicles are 5.

Therefore, it can be written as:

  $x+y=5$

In van 7 people can sit so total persons in van is $7x$ .

In sedan total five people can sit so total person in sedan is $5y$

Total person that either sit in van or sedan are 31.

Hence equation obtained

  $7x+5y=31$ .

Thus, the system of equation is

  $\begin{array}{l}x+y=5\mathrm{....}(1)\\ 7x+5y=\mathrm{31...}(2)\end{array}$

Multiply equation (1) by 7 it becomes:

  $7x+7y=\mathrm{35...}(3)$

Now subtract equation (2) from (3):

  $\begin{array}{l}7x-7x+7y-5y=35-31\\ 0+2y=4\\ 2y=4\\ y=\frac{4}{2}\\ y=2\end{array}$

Substitute the value of $y$ in equation (1):

  $\begin{array}{l}x+2=5\\ x=5-2\\ x=3\end{array}$

The number of van are 3 and number of sedan are 2.