SOLUTION: cantrell associastes a real estate developer is planning to build a new apartment complex consisting of one -bedroom aunits and two -and three

SOLUTION: cantrell associastes a real estate developer is planning to build a new apartment complex consisting of one -bedroom aunits and two -and three - bedroom townhouses. a total of 19

Question 116354: cantrell associastes a real estate developer is planning to build a new apartment complex consisting of one -bedroom aunits and two -and three - bedroom townhouses. a total of 192 units are planned and the number of family units two and three bedroom townhouses will equal the number of one bedroom units. If the number of one bedroom units will be 3 times the number of three bedroom units find how many units of each type will be in the complex
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apartment complex consisting of one-bedroom units and two and three-bedroom townhouses. a total of 192 units are planned and the number of family units, two and three bedroom townhouses, will equal the number of one bedroom units. If the number of one bedroom units will be 3 times the number of three bedroom units find how many units of each type will be in the complex
:
Let x = no. of 1 br units
Let y = no. of 2 br units
Let z = no. of 3 br units
:
It says,"two and three bedroom townhouses will equal the number of one bedroom units." An equation for this:
x = y + z
:
"the number of one bedroom units will be 3 times the number of three bedroom units"
x = 3z
Substitute (y + z) for x (from the 1st statement)
y + z = 3z
y = 3z - z
y = 2z
:
The total apt equation:
x + y + z = 192
:
Substitute 3z for x; and 2z for y; find z
3z + 2z + z = 192
6z = 192
z = 192/6
z = 32 ea 3 br units
then
x = 3(32) = 96 1 br units
y = 2(32) = 64 2 br units
:
Check solutions: 32 + 64 + 96 = 192

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