Final answer:
The two services will cost the same after 15 months, and the cost at that time will be $525 for both options.
Step-by-step explanation:
To find out when the two options will cost the same, we need to set up an equation.
Let's denote the number of months as 'x'.
For the first option, the cost will be $150 (the dish) plus $25 per month (service). So the cost will be 150 + 25x.
For the second option, the cost will be $35 per month (service and dish rental). So the cost will be 35x.
We can set up the equation 150 + 25x = 35x to find when the costs are equal.
Subtracting 25x from both sides, we get 150 = 10x.
Dividing both sides by 10, we get x = 15.
Therefore, the two services will cost the same after 15 months.
To find the cost at that time, we can substitute x = 15 into either option.
Using the first option, the cost will be 150 + 25 * 15 = $525.
Using the second option, the cost will be 35 * 15 = $525.