Question

you are choosing between two different cell phone plans. the first plan charges a rate of 23 cents per minute. the second plan charges a monthly fee of \\$39.95 plus 12 cents per minute.

how many minutes would you have to use in a month in order for the second plan to be preferable?

Explanation:

⚡ Using what you learned: Creating Equations to Model Relationships

Step 1: Define variables and write cost equations

Let \( m \) be the number of minutes used in a month.

Convert all monetary values to the same unit (dollars):

• Plan 1: \( 23 \) cents per minute = \( \$0.23 \) per minute.
• Plan 2: \( \$39.95 \) monthly fee plus \( 12 \) cents (\( \$0.12 \)) per minute.

Write the cost equations for both plans:

$$ C_1 = 0.23m $$

$$ C_2 = 39.95 + 0.12m $$

Step 2: Set up the inequality

For the second plan to be preferable, its cost must be strictly less than the cost of the first plan:

$$ C_2 < C_1 $$

$$ 39.95 + 0.12m < 0.23m $$

Step 3: Solve for \( m \)

Subtract \( 0.12m \) from both sides:

$$ 39.95 < 0.11m $$

Divide both sides by \( 0.11 \):

$$ m > \frac{39.95}{0.11} $$

$$ m > 363.1818... $$

Since minutes are typically billed as whole numbers, you must use at least \( 364 \) minutes for the second plan to be cheaper.

Answer:

More than 363 minutes (or at least 364 minutes)