Chapter 7, Problem 9PS

To determine

To find: the cost of four-foot cable.

Answer to Problem 9PS

The cost of four foot cable is $12.

Explanation of Solution

Given information:

A six-foot cable for $15.50 and a three-foot cable for $10.25. The cost of cable is the sum of the cost of the two connections and the cost of the cable itself.

Calculation:

Let $x$ be the proportionate length of six foot cable and $y$be the proportionate length of three foot cable needed to make the needed four foot cable.

So the equations can be:

  $\begin{array}{l}x+y=\mathrm{1...........}(1)\\ 6x+3y=\mathrm{4........}(2)\end{array}$

Multiply the first equation(1) with 3 and subtract from equation (2).

  $\begin{array}{c}6x+3y=4\\ 3x+3y=3\\ 3x=1\\ x=\frac{1}{3}\end{array}$

The value of $y$from equation (1) is $y=\frac{2}{3}$ .

The cost of six foot cable is given as $15.50 and that of three foot cable is $10.25.

So the total cost of four foot cable would be:

  $c=15.5x+10.25y\mathrm{..............}(3)$

Substituting the values of $x$ and $y$ , we get

  $\begin{array}{c}c=15.50\left(\frac{1}{3}\right)+10.25\left(\frac{2}{3}\right)\\ =5.167+6.833\\ =12\end{array}$

So the cost of four foot cable is $12.