Question

you are choosing between two different cell phone plans. the first plan charges a rate of 19 cents per minute. the second plan charges a monthly fee of $34.95 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? round up to the nearest whole minute.

Explanation:

Step1: Set up cost - equations

Let $x$ be the number of minutes used in a month. The cost $C_1$ of the first plan is $C_1 = 0.19x$ (since 19 cents = $0.19$ dollars). The cost $C_2$ of the second plan is $C_2=34.95 + 0.09x$ (since 9 cents = $0.09$ dollars and the monthly fee is $34.95$ dollars).

Step2: Set up inequality

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

Step3: Solve the inequality

Subtract $0.09x$ from both sides: $34.95<0.19x - 0.09x$. Simplify the right - hand side to get $34.95 < 0.1x$.

Step4: Isolate $x$

Divide both sides of the inequality by $0.1$: $x>\frac{34.95}{0.1}$. Calculate $\frac{34.95}{0.1}=349.5$.

Answer:

350