Chapter 3.4, Problem 31P

To determine

the base price of the car.

Answer to Problem 31P

  $21800$ $

Explanation of Solution

Given: with the major option package and destination charge, car costs $24416$ $.

The price of car was ten times the major option charge and fifty times the destination charge.

Calculation:

Let price of base price be B , major option package be M and destination charge be D.

Equation for total cost is.

  $B+M+D=24416$ …… (1)

Since, the base price of car was ten times the major option charge therefore.

  $B=10M$

  $M=\frac{B}{10}$ …… (2)

And base price of car is fifty times the destination charge therefore.

  $B=50D$

  $D=\frac{B}{50}$ …… (3)

Substituting $M=\frac{B}{10}$ and $D=\frac{B}{50}$ in equation (1).

  $\begin{array}{l}B+M+D=24416\\ B+\frac{B}{10}+\frac{B}{50}=24416\\ \frac{56B}{50}=24416\\ B=21800\end{array}$

Major option package charge is.

From equation (2).

  $\begin{array}{l}M=\frac{B}{10}\\ M=\frac{21800}{10}\\ M=2180\end{array}$

Destination charge is.

From equation (3).

  $\begin{array}{l}D=\frac{B}{50}\\ D=\frac{21800}{50}\\ D=436\end{array}$

Therefore, the price of base price is $21800$ .