Chapter MPS, Problem 1.12MPS

(a)To Find: Inequality of the given problem

To determine

Answer to Problem 1.12MPS

  $\$48+\$0.01\left(x\right)<\$58$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Per month plan cost}=\$48\\ \text{cost for extra use}=\$0.01\text{ per kilobyte}\end{array}$

Formula Used:

  $\text{monthly plan cost}+\text{cost for extra use}=\text{total cost}$

Calculation:

  $\begin{array}{l}\text{Let }x\text{ be the extra kilobyte that melissa go beyond her free uses}\text{.}\\ \text{→}\text{Handheld device service monthly plan cost}=\$48\\ \text{→}\text{cost for every kilobyte beyond the free uses}=\$0.01\\ \text{→}\text{Total payment paid by Melissa is less than }\$58\\ \text{⇒}\text{Inequality for the given data is :}\\ \text{→}\text{ monthly plan cost}+\text{cost for extra use}<\$58\\ \text{⇒}\$48+\$0.01\left(x\right)<\$58\end{array}$

Conclusion:

(b)

To determine

To Find: solution of the inequality

Answer to Problem 1.12MPS

  $x<100$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Per month plan cost}=\$48\\ \text{cost for extra use}=\$0.01\text{ per kilobyte}\end{array}$

Formula Used:

  $\text{monthly plan cost}+\text{cost for extra use}=\text{total cost}$

Calculation:

  $\begin{array}{l}\text{→}\text{ monthly plan cost}+\text{cost for extra use}<\$58\\ \text{⇒}\$48+\$0.01\left(x\right)<\$58\\ \text{⇒}\$48+\$0.01\left(x\right)-\$48<\$58-\$48\left(\text{subtract both side by }\$48\right)\\ \text{⇒}\$0.01\left(x\right)<\$10\left(\text{Divide both side by }\$0.01\right)\\ \text{⇒}x<100\end{array}$

Conclusion:

Melissa has to use less than $100$ kilobytes beyond her free uses so that she has to pay less than $\$58$