Explain and Show Work?

Question

REAL ESTATE: AMC Homes, Inc. is planning to build three- and four-bedroom homes in a housing development called Chestnut Hills. 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 home is $16,000 and from each four-bedroom home, $17,000. If AMC Home must net a total profit of $13.4 million from this development, how many homes of each type should they build?

Answer 1

No. of three-bedroom homes = x
Therefore, No. of four-bedroom homes = 3x
Profit from three-bedroom homes = 16000x
Profit form four-bedroom homes = 17000*3x
16000x + 51000x = 13.4 * 10^6
67*10^3x = 13.4*10^6
67x = 13.4*10^3
or x = 200
No. of three-bedroom homes = 200
No. of four-bedroom homes = 3*200 = 600

Answer 2

Set up a system of equations

x = three bedroom homes
y= four bedroom homes

y = 3x
16000x + 17000y = 13400000

Substitute 3x in for y in the second equation

16000x + 51000x = 13400000
66000x = 13400000
x = 203

y = 3 * 203
y = 609
203 - three bedroom homes
609 - four bedroom homes

Answer 3

Amc Chestnut Hill

Answer 4

Here we go.

General Statements:

#4BDR = 3 x #3BDR
3PROF = 16,000
4PROF = 17,000

Total Value Equation:

(#4BDR X 4PROF) + (#3BDR X 3PROF) = 13,400,000

Work:

(3 X #3BDR X 4PROF) + (#3BDR X 3PROF) = 13,400,000
(3 X #3BDR X 17,000) + (#3BDR X 16,000) = 13,400,000
51,000 X #3BDR + 16,000 X #3BDR = 13,400,000
67,000 X #3BDR = 13,400,000
#3BDR = 200
#4BDR = 3 X 200 = 600