Bob is looking for internet service for his new apartment. If he continues with his old internet provider, he will pay $65 per month and receive a $50 customer loyalty credit. The new internet provider he is considering will charge a one-time installation fee of $150, plus $40 per month.

Question

After how many months would the two options cost the same?
months

Answer 1

To determine after how many months the two internet service options would cost the same, we can set up an equation based on the costs of each option.

1. Old provider's total cost:

   • Monthly cost: $65
   • Loyalty credit: $50 per month
   • Therefore, the effective monthly cost is: \[ 65 - 50 = 15 \text{ dollars per month} \]
   • If Bob stays with his old provider for \( m \) months, the total cost will be: \[ C_{\text{old}} = 15m \]

2. New provider's total cost:

   • One-time installation fee: $150
   • Monthly cost: $40
   • Therefore, for \( m \) months, the total cost will be: \[ C_{\text{new}} = 150 + 40m \]

3. Setting the costs equal to find when they are the same: \[ 15m = 150 + 40m \]

4. Rearranging the equation: \[ 15m - 40m = 150 \] \[ -25m = 150 \] \[ m = \frac{150}{25} = 6 \]

Thus, the two options would cost the same after 6 months.