Allegra has a cell-phone plan that charges $65 per month and $0.10 for every minute that she uses the phone beyond what her plan allows. One month, she was billed $73.40.

a. Define a variable for the unknown.
b. Write an equation to model the problem. Explain your answer.
c. Solve the equation. Show your work.
d. Find the number of minutes that Allegra went over the time that the plan allows. Explain your answer.

Jullian, Mary -- please use the same name for your posts.

I didn't not appreciate you impersonating me in another post!!!!!

a. Let's define the unknown as "x," representing the number of minutes that Allegra went over the time that the plan allows.

b. To write an equation to model the problem, we need to consider the total cost for the month, which includes the fixed monthly charge of $65 and the additional charge for going over the time allowed. The additional charge is $0.10 per minute. Thus, the equation would be:

$65 + $0.10x = $73.40

We add the fixed monthly charge and the charge for the extra minutes to get the total cost.

c. To solve the equation, we need to isolate the variable "x" on one side of the equation.

Subtracting $65 from both sides of the equation:

$0.10x = $73.40 - $65
$0.10x = $8.40

Next, divide both sides of the equation by $0.10:

x = $8.40 / $0.10
x = 84

So, Allegra went over the time allowed by 84 minutes.

d. To find the number of minutes Allegra went over the time allowed, we need to look at the value of "x," which we found to be 84. Therefore, Allegra went over the time allowed by 84 minutes.