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6 March, 20:51

Cantwell Associates, a real estate devel - oper, is planning to

build a new apartment complex con - sisting ofone-bedroomunits and

two - and three-bedroom townhouses. A total of192 units is planned,

and the number of family units (two - andthree-bedroom town - houses)

will equal the number of one-bedroomunits. If the number of

one-bedroom units will be three times thenumber of three-bedroom

units, find how many units of each typewill be in the complex.

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Answers (1)
  1. 6 March, 21:36
    0
    number of 1 bedroom units are 96

    number of 1 bedroom units are 64

    number of 1 bedroom units are 32

    Step-by-step explanation:

    Let the number of 1 bedroom units be 'a'

    number of 2 bedroom units be 'b'

    and,

    number of 3 bedroom units be 'c'

    now,

    according to the question

    a + b + c = 192 ... (1)

    also,

    b + c = a ... (2)

    and,

    a = 3c ... (3)

    now,

    substituting value of 'a' from 3 into 2, we get

    b + c = 3c

    or

    b = 2c ... (4)

    also,

    from 3 and 1

    3c + b + c = 192

    or

    4c + b = 192 ... (5)

    now from 4 and 5,

    4c + 2c = 192

    or

    6c = 192

    or

    c = 32 units

    now, substituting c in equation 4, we get

    b = 2 * 32 = 64 units

    and, substituting c in equation (3), we get

    a = 3 * 32 = 96 units

    Therefore,

    number of 1 bedroom units are 96

    number of 1 bedroom units are 64

    number of 1 bedroom units are 32
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