Long distance Phone Company A charges a base rate of $5.00 per month plus 4 cents a minute that you're on the phone. Long distance Phone Company B charges a base rate of only $2.00 per month but they charge 10 cents per minute used. How much time per month would you have to talk on the phone before subscribing to Company A would save you money?

5 + .04t < 2 + .10t

3 < .06t

t > 3/.06 = 50

To determine the threshold at which subscribing to Company A would save you money compared to Company B, we need to set up an equation.

Let's assume x represents the number of minutes you talk on the phone per month.

For Company A, the total monthly cost is calculated as:
Cost_A = $5.00 (base rate) + 0.04x (4 cents per minute)

For Company B, the total monthly cost is calculated as:
Cost_B = $2.00 (base rate) + 0.10x (10 cents per minute)

Now, we need to find the value of x where Cost_A becomes less than Cost_B:

$5.00 + 0.04x < $2.00 + 0.10x

Simplifying the equation:

0.04x - 0.10x < $2.00 - $5.00

-0.06x < -$3.00

Dividing both sides by -0.06 (note that dividing by a negative number reverses the inequality):

x > -$3.00 / -0.06

x > 50

Therefore, if you talk on the phone for more than 50 minutes per month, subscribing to Company A would save you money compared to Company B.

To determine how much time per month you would have to talk on the phone before subscribing to Company A would save you money, we need to compare the costs of both companies based on the given information.

For Company A:
- Base rate: $5.00 per month
- Additional cost: 4 cents per minute

For Company B:
- Base rate: $2.00 per month
- Additional cost: 10 cents per minute

Let's assume the amount of time per month you talk on the phone is represented by T (in minutes).

Cost with Company A:
Base rate + (Additional cost per minute x T) = $5.00 + ($0.04 x T) = $5.00 + 0.04T

Cost with Company B:
Base rate + (Additional cost per minute x T) = $2.00 + ($0.10 x T) = $2.00 + 0.10T

To find out when Company A becomes cheaper, we need to set up an equation and solve for T:

$5.00 + 0.04T = $2.00 + 0.10T

Subtracting $2.00 from both sides:

$3.00 + 0.04T = 0.10T

Subtracting 0.04T from both sides:

$3.00 = 0.06T

Dividing both sides by 0.06:

$3.00 / 0.06 = T

T ≈ 50

So, you would have to talk for approximately 50 minutes per month for Company A to save you money compared to Company B.

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