SOLUTION: A​ person's website specializes in the sale of rare or unusual vegetable seeds. He sells packets of​ sweet-pepper seeds for ​$2.48 each and packets of​ hot-
Algebra ->
Customizable Word Problem Solvers
-> Mixtures
-> SOLUTION: A​ person's website specializes in the sale of rare or unusual vegetable seeds. He sells packets of​ sweet-pepper seeds for ​$2.48 each and packets of​ hot-
Log On
Question 1095642: A person's website specializes in the sale of rare or unusual vegetable seeds. He sells packets of sweet-pepper seeds for $2.48 each and packets of hot-pepper seeds for $4.72 each. He also offers a 16-packet mixed pepper assortment combining packets of both types of seeds at $2.76 per packet. How many packets of each type of seed are in the assortment?
There are _____ packets of sweet-pepper seeds and
________ packets of hot-pepper seeds. Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website! Before we do anything else, let's think about what a reasonable answer should be. (That's ALWAYS a good thing to do when solving a math problem!)
The $2.76 per packet price of the assortment is much closer to the $2.48 price for the sweet pepper seeds than it is to the $4.72 price for the hot pepper seeds. So the assortment should contain far more sweet pepper seed packets than hot pepper seed packets.
Algebraically, we can do this....
let x = the number of sweet pepper seed packets
then (16-x) = the number of hot pepper seed packets
The cost of the sweet pepper seed packets is then 2.48x; the cost of the hot pepper seed packets is 4.72(16-x).
The cost of the assortment is 2.76(16).
So...
ouch... calculator time!
The assortment contains 14 packets of sweet pepper seeds and 2 packets of hot pepper seeds.
Now here is an alternative method for solving any type of "mixture" problems that, if you understand it, will get you to the answer much faster and with far less work.
The key idea behind this method is that the ratio in which the two ingredients (in this problem, the two kinds of seed packets) are mixed is exactly determined by where the cost per packet in the assortment lies between the costs per packet of the two ingredients.
Here is the arithmetic for your problem using this method:
4.72 - 2.76 = 1.96 [how far the price per packet in the assortment is from the cost per packet of the hot pepper seed]
2.76 - 2.48 = 0.28 [how far the price per packet in the assortment is from the cost per packet of the sweet pepper seed]
1.96:0.28 = 7:1 [the ratio of those two, simplified]
These calculations show that there should be 7 sweet pepper seed packets for each hot pepper seed packet.
And with 16 packets in the assortment, that means 14 packets of sweet pepper seeds and 2 packets of hot pepper seeds.
Now compare the calculations required there to the calculations we had to go through with the traditional algebraic solution....
