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10 July, 10:00

The build a dream construction company has plans for two models of the homes they build, model a and model b. The model a home requires 18 single windows and 3 double windows. The model b home requires 20 single windows and 5 double windows. A total of 1,800 single windows and 375 double windows have been ordered for the developments. Write and solve a system of equations to represent this situation. Define your variables. Interpet the solution of the linear system in terms of the problem situation

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  1. 10 July, 10:02
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    a = 50 houses

    b = 45 houses

    Step-by-step explanation:

    Given

    Number of houses called Model A = a

    Number of houses called Model B = b

    Total of single windows = 1800

    Total of double windows = 375

    then we have the system of equations

    18a + 20b = 1800 (I)

    3a + 5b = 375 (II)

    Solving the system by whatever method we prefer, we obtain

    (I) a = (1800 - 20b) / 18

    then (II)

    3 ((1800 - 20b) / 18) + 5b = 375

    ⇒ 300 - (10/3) * b + 5b = 375

    ⇒ (5/3) * b = 75

    ⇒ b = 45 houses

    then

    a = (1800 - 20*45) / 18

    ⇒ a = 50 houses
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