While solar energy powered home systems are quite expensive to install, adding some passive energy features to conventional construction can make a substantial reduction in heating and cooling costs. Passive solar requires no machinery and uses the building itself to collect, store and distribute solar energy. An excellent passive solar investment is the installation of better quality windows with high resistance to heat transmission, provided with exterior shading on the south side to cut off high angled sun rays in cooling season and let in low angled winter sun during heating season.

cost of conventional HVAC system: $11300
annual cost for HVAC in conventional house: $1290
extral installation for better Windows & shading: $2600
Annual cost for HVAC in improved house: $840
Conventional=__?__
Improved=__?__

11300+1290n

C-conventional = 11300+1290n

C-improved = 13900+840n
(notice its not 2600 bc it asks basically for total cost over years for improved house, so thats 11300+2600= 13900)

If you want to find out when they equal the same cost, equal the two equations together

11300+1290n= 13900+840n
n= 5.8 if you round to the nearest one decimal

To calculate the cost of the conventional house, we need to know the initial cost of the HVAC system and the annual cost for operating it.

Given:
Cost of conventional HVAC system = $11,300
Annual cost for HVAC in conventional house = $1,290

Therefore, the cost of the conventional house can be calculated as the sum of the initial cost of the HVAC system plus the annual cost for operating it over a certain period.

Conventional House Cost = Cost of HVAC system + (Annual cost for HVAC x Number of years)

To calculate the cost of the improved house, we need to consider the additional installation cost for better windows and shading and the reduced annual cost for operating the HVAC system.

Given:
Additional installation cost for better windows & shading = $2,600
Annual cost for HVAC in improved house = $840

Therefore, the cost of the improved house can be calculated as the sum of the additional installation cost for windows and shading plus the reduced annual cost for operating the HVAC system over a certain period.

Improved House Cost = Additional installation cost for windows & shading + (Annual cost for HVAC x Number of years)

Please provide the number of years for which you would like to calculate the costs of the conventional and improved houses.