Chapter 12.4, Problem 40PPS

To determine

To explain:

The less expensive option.

Answer to Problem 40PPS

The second contractor is the better deal.

Explanation of Solution

Given information:

Mr. Thomas is planning to remove an old patio and install a new rectangular concrete patio $20$ feet long, $12$ feet wide, and $4$ inches thick. One contractor bid $\$2225$ for the project. A second contractor bid $\$500$ per cubic yard for the new patio and $\$700$ for removal of the old patio.

First convert inches in feet.

Formula: divide the length value by $12$

  $\begin{array}{c}4\text{ in}=\frac{4}{12}\\ =\frac{1}{3}\text{ ft}\end{array}$

Volume of the new patio is as follows:

  $V=lwh$

Substitute $l=20$ , $w=12$ and $h=\frac{1}{3}$ in the above formula.

  $\begin{array}{c}V=20\cdot 12\cdot \frac{1}{3}\\ =20\cdot 4\\ =80{\text{ ft}}^3\end{array}$

  $1$ yard cubed is ${\text{27 ft}}^3$ .

The cost for the cement work is:

  $80{\text{ ft}}^3\cdot \frac{1{\text{ yd}}^3}{27{\text{ ft}}^3}\cdot \frac{\$500}{1{\text{ yd}}^3}=\$1481.48$

The cost of removal of old cement is:

  $\$1481.48+\$700=\$2181.48$

The second contractor is the better deal.