document.write( "Question 417859: I have a word problem that I am not sure how to put into an algebraic equation(s):\r
\n" ); document.write( "\n" ); document.write( "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?\r
\n" ); document.write( "\n" ); document.write( "My instructor did not cover any word problems even close to this one, so if anyone could help me with this I would appreciate it. It is due Tuesday. \n" ); document.write( "
Algebra.Com's Answer #292489 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Peter can buy a high-efficiency furnace for $2250 that costs $412 per year to operate.
\n" ); document.write( " He may also buy a standard furnace for $1710 that costs $466 per year to operate.
\n" ); document.write( "Find how long it will take for the two furnaces to have the same cost.
\n" ); document.write( " If Peter intends to live in his house for 7 years which furnace should he buy?
\n" ); document.write( " What if he wants to live in his house for 20 years?
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\n" ); document.write( "Let y = no. of years that he will use the furnace
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\n" ); document.write( "Write a cost equation for each furnace:
\n" ); document.write( "C(y) = 412y + 2250; (High Efficiency)
\n" ); document.write( "and
\n" ); document.write( "C(y) = 466y + 1710; (Standard)
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\n" ); document.write( "To find when the costs are equal:
\n" ); document.write( "Standard = High Efficiency
\n" ); document.write( "466y + 1710 = 412y + 2250
\n" ); document.write( "466y - 412y = 2250 - 1710
\n" ); document.write( "54y = 540
\n" ); document.write( "y = \"540%2F54\"
\n" ); document.write( "y = 10 yrs, they will cost the same
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\n" ); document.write( "You can confirm this by substituting 10 for y in both equations
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\n" ); document.write( "You can see if he only lives there 7 yrs, the standard would be cheaper.
\n" ); document.write( "However, in 20 yrs the high efficiency furnace would make sense
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\n" ); document.write( "prove this to yourself, calculate the total cost when y=7 for both furnaces
\n" ); document.write( "do the same for y=20.
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