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23 April, 05:55

The shamrock inn offers two holiday weekend specials. The first 2 nights and 4 meals for $205, while the other is 3 nights and 8 meals for $342.50. At these rates, what is the room rate and cost of a meal?

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  1. 23 April, 08:53
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    The answer to your question is Night = $ 67.5, meal = $17.5

    Step-by-step explanation:

    Data

    Night = n

    Meal = m

    2n + 4m = $205 (I)

    3n + 8m = $342.5 (II)

    Process

    1. - Solve the system of equations by elimination

    Multiply equation I by (3) and equation II by (-2)

    6n + 12m = 615

    -6n - 16m = - 685

    Sum the equations

    0 - 4m = - 70

    m = - 70 / - 4

    m = 17.5

    2. - Find the value of n, substitute m in equation I

    2n + 4 (17.5) = 205

    2n + 70 = 205

    2n = 205 - 70

    2n = 135

    n = 135 / 2

    n = 67.5
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