SOLUTION: A​ person's website specializes in the sale of rare or unusual vegetable seeds. He sells packets of​ sweet-pepper seeds for ​$2.32 each and packets of​ hot-pepper seeds for

Algebra ->  Equations -> SOLUTION: A​ person's website specializes in the sale of rare or unusual vegetable seeds. He sells packets of​ sweet-pepper seeds for ​$2.32 each and packets of​ hot-pepper seeds for      Log On


   

Question 1165370: A​ person's website specializes in the sale of rare or unusual vegetable seeds. He sells packets of​ sweet-pepper seeds for ​$2.32 each and packets of​ hot-pepper seeds for ​$4.56 each. He also offers a 16​-packet mixed pepper assortment combining packets of both types of seeds at ​$2.88 per packet. How many packets of each type of seed are in the​ assortment?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x of xweet-pepper packets
h of hot-pepper packets
system%28x%2Bh=16%2C2.32x%2B4.56h=2.88%2A16%29
.
.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If a formal algebraic solution is not required, here is a quick and easy way to solve any 2-part mixture problem like this.

(1) Find where the per-packet price for the mixture lies between the per-packet prices of the two types of seeds.

4.56-2.32 = 2.24
2.88-2.32 = 0.56
0.56/2.24 = 1/4

The per-packet price for the mixture is one-fourth of the way from $2.24 to $4.56.

(2) That means 1/4 of the packets in the assortment are packets of the higher-priced seed.

ANSWER: 1/4 of 16 packets, or 4 packets, of the hot-pepper seeds; the other 12 packets are of sweet-pepper seeds.

CHECK:
12(2.32)+4(4.56) = 27.84+18.24 = 46.08
16(2.88) = 46.08