Question

A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the customer pays 6 cents per minute of use. In Plan B, the customer pays a monthly fee of $6 and then an additional 4 cents per minute of use.For what amounts of monthly phone use will Plan A cost more than Plan B?Use m for the number of minutes of phone use in a month, and solve your inequality for m.

Answer 1

Given:

Plan A

- no monthly fee

- $0.06 per minute of use

Plan B

- $6 monthly fee

- $0.04 per minute of use

Find: number of minutes where the cost of Plan A > cost of Plan B

Solution:

Let's create an equation for each plan's cost per month.

Let m = number of minutes of phone use

Plan A's cost = 0.06m

Plan B's cost = 0.04m + 6

For the inequality cost of Plan A > cost of Plan B, this can be written as:

`0.06m>0.04m+6`

From this, we can solve for "m".

Subtract 0.04 m on both sides of the inequality.

`\begin{gathered} 0.06m-0.04m>0.04m-0.04m+6 \\ 0.02m>6 \end{gathered}`

Divide both sides of the equation by 0.02.

`\begin{gathered} (0.02m)/(0.02)>(6)/(0.02) \\ m>300 \end{gathered}`

Therefore, when the number of minutes of phone use is greater than 300, the monthly cost of Plan A will be more than the monthly cost of Plan B.