Final answer:
The costs of the AT&T "One Rate" and "One Rate Plus" plans are the same when 99 minutes are used, which equates to a cost of $14.85 for both plans.
Step-by-step explanation:
To find when the costs of the two calling plans offered by AT&T in 1997, "One Rate" and "One Rate Plus," are the same, we set up an equation where the cost of each plan is equal. We will define x as the number of minutes used, and y as the total cost.
The "One Rate" plan's cost is $0.15 per minute, so the equation for this plan is y = 0.15x.
The "One Rate Plus" plan includes a service fee of $4.95 per month, plus $0.10 per minute. So, the equation for this plan is y = 4.95 + 0.10x.
To find when the costs are the same, set the two equations equal to each other:
0.15x = 4.95 + 0.10x. To solve for x, first subtract 0.10x from both sides to get 0.05x = 4.95. Then, divide both sides by 0.05 to find the number of minutes where both plans cost the same: x = 99.
At 99 minutes, we can plug this back into either equation to find the cost, which gives us y = 0.15 * 99 = $14.85.
So, at 99 minutes, the costs of the AT&T "One Rate" plan and the "One Rate Plus" plan are both $14.85.