Final answer:
To determine when the natural gas grill becomes cheaper, calculate the point where the total costs of both grills are equal.
Step-by-step explanation:
When comparing the costs of the propane grill and the natural gas grill, we can calculate the break-even point to determine after how many years the latter becomes the cheaper option. Let's denote the initial cost and the yearly cost for the propane grill as Cp and Yp, respectively, and for the natural gas grill as Cng and Yng respectively.
The total cost for the propane grill after t years will be Cp + Yp × t. The total cost for the natural gas grill after t years will be Cng + Yng × t.
To find out after how long the natural gas grill is cheaper, we set Cp + Yp × t equal to Cng + Yng × t and solve for t:
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- Cp + Yp × t = Cng + Yng × t
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- 250 + 40t = 340 + 25t
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- 15t = 90
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- t = 6
Therefore, after 6 years, the natural gas grill becomes the more economical choice.