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Using solar energy, the total cost to heat a house includes an installation fee of $7,000 with an average cost of $280 per year. Usingconventional fuel, the total cost to heat the same house includes an installation fee of $4,000 and an average cost of $580 per year.How many years until the total costs are the same for each?

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Solution

For this case we can define

x= number of years

And we can create the following equation to solve the problem

7000 + 280 x = 4000 + 580x

And then we can solve for x like this:

7000 -4000 = 580x - 280 x

3000 = 300x

x= 3000/300 =10

So then the answer would be 10 years

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