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6 December, 00:15

Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units, two-bedroom townhouses, and three-bedroom townhouses. A total of 216 units is planned. The total number of 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 townhouses, find how many units of each type will be in the complex. one-bedroom units units two-bedroom townhouses units three-bedroom townhouses units

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  1. 6 December, 02:46
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    108 one-bedroom units

    72 two-bedroom units

    36 three-bedroom units

    Step-by-step explanation:

    Let x, y, z the number of one-bedroom, two-bedroom and three-bedroom units respectively. Then

    1) x+y+z = 216

    2) y+z = x

    3) x = 3z

    Multiplying equation 1) by - 1 and adding it to 2), we get

    -x = x-216 so, x = 216/2 = 108

    x = 108

    Replacing this value in 3) we get

    z = 108/3 = 36

    z = 36

    Replacing now in 2)

    y+36 = 108, y = 108-36 and

    y = 72
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