Internet rates for two companies are shown in the table. After how many months of
service is the total cost the same no matter which company is used? What is this total
cost?
Intemet Service Provide
Charges

Tyson's Ethernet $100 activation fee plus $20 per month

Darriana's DSL
$30 per month


A 10 months, $300

B 20 months, $600

C 30 months, $700

D 2 months, $60

100+(20×10)=300

30×10 =300

months = 10

The total cost becomes the same after 20 months of service, and the total cost is $600.

To find out when the total cost becomes the same for both companies, we need to compare their cumulative costs over time.

Tyson's Ethernet has an activation fee of $100 plus $20 per month, while Darriana's DSL costs $30 per month.

Let's set up equations for both companies:

For Tyson's Ethernet:

Total cost = Activation fee + Monthly charges

Total cost = $100 + ($20/month) * months

For Darriana's DSL:

Total cost = Monthly charges

Total cost = ($30/month) * months

We want to find when these two total costs are equal:

$100 + ($20/month) * months = ($30/month) * months

Now we can solve for the number of months:

$100 + ($20/month) * months = ($30/month) * months

$100 = ($30/month - $20/month) * months

$100 = $10/month * months

months = $100 / $10

months = 10

So, it takes 10 months for the costs to be equal. Now let's find the total cost at that point:

Total cost = ($30/month) * months

Total cost = ($30/month) * 20 months

Total cost = $600

Therefore, after 20 months of service, the total cost is the same for both companies, and the total cost is $600.

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