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-pepper seeds for $4.88 each.
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-pepper seeds for $4.88 each.
Log On
Question 1198429: 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 $4.88 each. He also offers a 16-packet mixed pepper assortment combining packets of both types of seeds at $3.53 per packet How many packets of each type of seed are in the assortment? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52784) (Show Source):
You can put this solution on YOUR website! .
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 $4.88 each.
He also offers a 16-packet mixed pepper assortment combining packets of both types of seeds at $3.53 per packet
How many packets of each type of seed are in the assortment?
~~~~~~~~~~~~~~~
x packets at $2.48 and 16-x packets at #4.88.
Write the "money equation"
2.48x + 4.88*(16-x) = 3.53*16 dollars
Simplify and find x
2.48x + 4.88*16 - 4.88x = 3.53*16
2.48x - 4.88x = 3.53*16 - 4.88*16
x = = 9.
ANSWER. In the assortment, there are 9 packets at $2.48 and 16-9 = 7 packets at $4.88.
The solution from the other tutor shows a standard algebraic solution method for 2-part "mixture" problems like this.
Here is an alternative which is often far less work, if the numbers in the problem are "nice".
Look at the three prices per packet -- $2.48, $3.53, and $4.88 (on a number line, if it helps) -- and observe/calculate that $3.53 is 105/240 = 7/16 of the way from $2.48 to $4.88.
That means 7/16 of the packets in the mixed assortment are the higher-priced hot pepper seeds.
Then, since the mixed assortment contain 16 packets of seeds, it contains 7 packets of the hot pepper seeds and 9 packets of the sweet pepper seeds.
