SOLUTION: Hi I know how to solve systems of equations, but I'm having trouble setting this one up. It is a word problem. AMC Homes, Inc is planning to build three and four bedroom homes.

Question 504623: Hi I know how to solve systems of equations, but I'm having trouble setting this one up. It is a word problem.
AMC Homes, Inc is planning to build three and four bedroom homes. Consumer demand indicates a need for three times as many four-bedroom homes as for three-bedroom homes. The net profit from each three-bedroom is $16,000 and $17,000 for each four bedroom. If the total net profit is $13.4 million how many homes of each type should they build?
Thanks for any help you might have :)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
AMC Homes, Inc is planning to build three and four bedroom homes.
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Consumer demand indicates a need for three times as many four-bedroom homes as for three-bedroom homes.
Let "f" be # of four-bedroom homes
Let "t" be # of three-bedroom homes.
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f = 3t
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The net profit from each three-bedroom is $16,000 and $17,000 for each four bedroom. If the total net profit is $13.4 million
16000t + 17000f = 13,400,000
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Substitute for "f" and solve for "t":
16000t + 17000(3t) = 13,400,000
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Divide thru by 1000 to get:
16t + 17(35) = 13.499
--
16t + 51t = 13,400
67t = 13,400
t = 200 (# of three-bedroom houses to build)
---
Solve for "f":
f = 35
f = 3*200 = 600 (# of four-bedroom houses to build)
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Cheers,
Stan H.
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how many homes of each type should they build?

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