Question

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?

Answer 1

7 packets of sweet-pepper seeds and 9 packet of hot-pepper seeds.

Step-by-step 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.