Question

Imagine you build a house and for heating systems you have a choice between solar and air heated by natural gas. The solar heating system costs $30,000 to install, with annual operating of cost of $150 per year afterwards. The gas heating system costs $6,250 to install, with an expected annual operating cost of $1100 per year afterwards. How could you use a system of equations to solve for the time when both systems would be the same cost? How many years would that be and what is the common cost? Which system would you want?

Answer 1

X represents years. Set the amounts equal.

$30,000 + $150(x) = $6,250 + $1100(x)

$23,750 = $950(x)

x = 25 years

Second part:

$30,000 + $150(25) = $33,750

$6,250 + $1100(x) = $33,750

Third part:

You would want the gas heating system if you were only going to have it for less than 25 years. Not completely sure what that question is asking.