Question

you are choosing between two different cell phone plans. the first plan charges a rate of 23 cents per minute. the second plan charges a monthly fee of $29.95 plus 9 cents per minute. how many minutes would you have to use in a month in order for the second plan to be preferable? question help: video submit question

Explanation:

Step1: Set up cost - functions

Let $x$ be the number of minutes used in a month. The cost $C_1$ of the first plan is $C_1 = 0.23x$ (since 23 cents = 0.23 dollars). The cost $C_2$ of the second plan is $C_2=29.95 + 0.09x$ (since 9 cents = 0.09 dollars and the monthly fee is 29.95 dollars).

Step2: Set up the inequality

We want to find when the second plan is preferable, i.e., when $C_2

Step3: Solve the inequality for $x$

Subtract $0.09x$ from both sides: $29.95<0.23x - 0.09x$.
Simplify the right - hand side: $29.95 < 0.14x$.
Divide both sides by 0.14: $x>\frac{29.95}{0.14}$.
Calculate $\frac{29.95}{0.14}\approx213.93$.
Since $x$ represents the number of minutes and it must be a whole number, we take $x = 214$.

Answer:

214