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31 January, 09:07

You are making gift baskets. each basket will contain three different types of candles: tapers, pillars ad jar candles. tapers cost $1 each, pillars cost $4 each, and jar candles cost $6 each. you put 8 candles costing a total of $24 in each basket, and you include as many tapers as pillars and jar candles combined. how many of each type of candle will be in a basket?

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  1. 31 January, 09:56
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    Let

    x = the number of tapers (each coss $1)

    y = the number of pillars (each costs $4)

    z = the number of jars (each costs $6)

    There are 8 candles in each basket, therefore

    x + y + z = 8 (1)

    The cost per basket is $24, therefore

    x + 4y + 6z = 24 (2)

    The number of tapers equals the sum of pillars and jars, therefore

    x = y + z (3)

    Substitute (3) into (1) and into (2).

    y + z + y + z = 8

    2y + 2z = 8

    y + z = 4 (4)

    y + z + 4y + 6z = 24

    5y + 7z = 24 (5)

    From (4), y = 4 - z. Substitute into (5).

    5 (4 - z) + 7z = 24

    2z + 20 = 24

    2z = 4

    z = 2

    y = 4 - z = 4 - 2 = 2

    x = y + z = 2 + 2 = 4

    Answer: 4 tapers, 2 pillars, 2 jars.
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