Question 417859
Peter can buy a high-efficiency furnace for $2250 that costs $412 per year to operate.
 He may also buy a standard furnace for $1710 that costs $466 per year to operate.
Find how long it will take for the two furnaces to have the same cost.
 If Peter intends to live in his house for 7 years which furnace should he buy?
 What if he wants to live in his house for 20 years? 
:
Let y = no. of years that he will use the furnace
:
Write a cost equation for each furnace:
C(y) = 412y + 2250; (High Efficiency)
and
C(y) = 466y + 1710; (Standard)
:
To find when the costs are equal:
Standard = High Efficiency
466y + 1710 = 412y + 2250
466y - 412y = 2250 - 1710
54y = 540
y = {{{540/54}}}
y = 10 yrs, they will cost the same
:
You can confirm this by substituting 10 for y in both equations
:
You can see if he only lives there 7 yrs, the standard would be cheaper.
However, in 20 yrs the high efficiency furnace would make sense
:
:
prove this to yourself, calculate the total cost when y=7 for both furnaces
do the same for y=20.