Chapter 2.3, Problem 29E

To determine

To calculate:

The inequality equation and solution that represents the cost of the carpet per square foot of new bedroom

Answer to Problem 29E

The inequality equation is $196x\le 700$ . The cost of the carpet per square foot of new bedroom is less than or equal to $\$3.57$ .

Explanation of Solution

Given information:

Cost: $\$700$

Calculation:

The given square sized bedroom has dimensions as side of $14ft$ :

  $a=14ft$

Consider,

  $x$ : cost of the carpet per square foot of new bedroom:

Need to write the inequality equation that represents the cost of the carpet per square foot of new bedroom:

  $Ax\le 700$  .. . . . (1)

Now, area of square is given as:

  $\begin{array}{l}A=a^2\\ A={\left(14\right)}^2\\ A=196f{t}^2\end{array}$

So, eq. (1) rewrite as:

  $\begin{array}{l}Ax\le 700\\ 196x\le 700\end{array}$

Divide by $196$ on both sides of above equation:

  $\begin{array}{l}196x\le 700\\ \frac{196}{196}x\le \frac{700}{196}\\ x\le 3.57\end{array}$

Therefore, cost of the carpet per square foot of new bedroom is less than or equal to $\$3.57$ .