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?

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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