Step 1:

(a)

Allegra has a cell phone plan of per month.

Beyond the plan, the paln charges for every minute.

Here the unknown variable is the number of minutes used after the plan.

Let  be the number of minutes used after the plan.

Step 2:

(b)

Allegra billed an amount of .

The total amount billed per month is sum of and for minutes.

The equation is .

Step 3:

(c)

The equation is .

Subtract 65 from both sides.

Apply additive inverse property: .

Divide each side by 0.1.

Therefore the value of is .

Step 4:

(d)

From (c): The value of is .

Therefore, Allegra uses minutes after her plan of per month and billed for a month.

Solution:

(a) be the number of minutes used after the plan.

(b) The equation is .

(c) The value of is .

(d) Allegra uses minutes after her plan of per month and billed for a month.