Today Star Satellite is offering the following special package to new customers: a one-time set-up fee of $10, the first month for free, and $32 per month thereafter. Which equation best represents k, the total cost of service for m months?

A k = (10 + m)32.
B k = 10 + 32m.
C k = 42(m – 1).
D k = 10 + 32(m – 1).

And what is your thinking, and why?

i think its D. because you add the one time fee and then the 32 per month then multiply by how many months minus one.

To find the equation that represents the total cost of service for a certain number of months, we need to consider the set-up fee, the free first month, and the subsequent monthly cost.

First, we have a one-time set-up fee of $10, which is a fixed cost and does not change with the number of months. So we start the equation with $10.

Next, the first month is free, so it does not add any cost for the customer.

After the first month, the customer is charged $32 per month. This cost is multiplied by the number of months, m.

Putting it all together, the equation that represents the total cost of service for m months is:

k = 10 + 32m

Therefore, the correct answer is:

B k = 10 + 32m.