Chapter MPS, Problem 1.11MPS

(a)To Find: Inequality of the given problem

To determine

Answer to Problem 1.11MPS

  $\$40+\$0.50\left(x\right)<\$65$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Per month plan cost}=\$40\\ \text{cost for extra minute}=\$0.50\text{ per min}\end{array}$

Formula Used:

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

Calculation:

  $\begin{array}{l}\text{Let }x\text{ be the number of minutes that frieda go beyond her free minutes}\text{.}\\ \text{→}\text{cell phone monthly plan cost}=\$40\\ \text{→}\text{cost for every minutes beyond the free minutes}=\$0.50\\ \text{→}\text{Total payment paid by Frieda is less than }\$65\\ \text{⇒}\text{Inequality for the given data is :}\\ \text{→}\text{ monthly plan cost}+\text{extra minutes cost}<\$65\\ \text{⇒}\$40+\$0.50\left(x\right)<\$65\end{array}$

Conclusion:

(b)

To determine

To Find: solution of the inequality

Answer to Problem 1.11MPS

  $x<50$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Per month plan cost}=\$40\\ \text{cost for extra minute}=\$0.50\text{ per min}\end{array}$

Formula Used:

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

Calculation:

  $\begin{array}{l}\text{→}\text{ monthly plan cost}+\text{extra minutes cost}<\$65\\ \text{⇒}\$40+\$0.50\left(x\right)<\$65\\ \text{⇒}\$40+\$0.50\left(x\right)-\$40<\$65-\$40\left(\text{subtract both side by }\$40\right)\\ \text{⇒}\$0.50\left(x\right)<\$25\left(\text{Divide both side by }\$0.50\right)\\ \text{⇒}x<50\end{array}$

Conclusion:

Frieda has to talk less than $50$ minutes beyond her free minutes so that she has to pay less than $\$65$