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6 September, 01:24

A person's website specializes in the sale of rare or unusual vegetable seeds. He sells packets of sweet-pepper seeds for $2.16 each and packets of hot-pepper seeds for $4.24 each. He also offers a 16 -packet mixed pepper assortment combining packets of both types of seeds at $3.33 per packet. How many packets of each type of seed are in the assortment?

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  1. 6 September, 03:39
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    7 packets of sweet-pepper seeds and 9 packet of hot-pepper seeds.

    Explanation:

    Let x packets of sweet-pepper seeds for $2.16 each and y packets of hot-pepper seeds for $4.24 each are mixed to obtain 16 -packet mixed pepper assortment for $3.33 per packet,

    i. e. x + y = 16 ... (1)

    Also,

    The price of sweet-pepper seeds + price of hot pepper seeds = price of the mixture

    ⇒ 2.16x + 4.24y = 3.33 (x+y)

    ⇒ 2.16x + 4.24y = 3.33x+3.33y

    ⇒ 2.16x + 4.24y - 3.33x-3.33y = 0

    ⇒ - 1.17x + 0.91y = 0 ... (2)

    Equation (2) + 1.17 * equation (1)

    0.91y + 1.17y = 18.72

    2.08y = 18.72

    ⇒ y = 9

    From equation (1),

    x + 9 = 16 ⇒ x = 16 - 9 ⇒ x = 7

    Hence, there are 7 packets of sweet-pepper seeds and 9 packet of hot-pepper seeds.
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