Question

you are choosing between two different cell phone plans. plan 1, charges a rate of 23 cents per minute. plan 2 charges a monthly fee of $44.95 plus 11 cents per minute.
if ( x = ) the number of minutes used and ( y = ) total cost in dollars.
a) write an equation to represent the total cost (in dollars) of each plan.
plan 1:
plan 2:
b) what is the minimum number of minutes you would have to use in a month in order for the second plan to be preferable?
minutes
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Explanation:

Step1: Write equations for Plan 1 and Plan 2

For Plan 1, since the rate is 23 cents per minute (\(0.23\) dollars per minute) and there is no monthly fee, the total cost \(y\) (in dollars) is \(y = 0.23x\).
For Plan 2, there is a monthly fee of \(44.95\) dollars and a rate of 11 cents per minute (\(0.11\) dollars per minute). So the total cost \(y\) (in dollars) is \(y=44.95 + 0.11x\).

Step2: Find when Plan 2 is preferable

We want to find when \(44.95+0.11x<0.23x\).
Subtract \(0.11x\) from both sides: \(44.95<0.23x - 0.11x\).
Simplify the right - hand side: \(44.95 < 0.12x\).
Divide both sides by \(0.12\): \(x>\frac{44.95}{0.12}\).
Calculate \(\frac{44.95}{0.12}=\frac{4495}{12}\approx374.58\).

Since \(x\) represents the number of minutes (and it must be an integer), we take the next whole number.

Answer:

A) Plan 1: \(y = 0.23x\); Plan 2: \(y=44.95 + 0.11x\)
B) \(375\) minutes