Question

you are choosing between two different cell phone plans. the first plan charges a rate of 26 cents per minute. the second plan charges a monthly fee of $44.95 plus 11 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 $C_1 = 0.26x$ (since 26 cents = 0.26 dollars). The cost $C_2$ of the second plan is $C_2=44.95 + 0.11x$ (since 11 cents = 0.11 dollars and there is a monthly fee of 44.95 dollars).

Step2: Set up the inequality

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

Step3: Solve the inequality

Subtract $0.11x$ from both sides: $44.95<0.26x - 0.11x$. Simplify the right - hand side: $44.95 < 0.15x$. Then divide both sides by 0.15: $x>\frac{44.95}{0.15}=\frac{4495}{15}=\frac{899}{3}\approx299.67$.

Answer:

$x > 299.67$, so you would have to use 300 minutes or more in a month for the second plan to be preferable.