Question

Ten pounds of mixed birdseed sells for 8.24 per pound. The mixture is obtained from two kinds of birdseed, with one variety priced at 5.68 per pound and the other at 8.88 per pound. How many pounds of each variety of birdseed are used in the mixture?

Answer 1

Answer:

2 pounds of 1st kind and 8 pounds of 2nd kind are mixed.

Explanation:

Given:

Ten pounds of mixed birdseed sells for 8.24 per pound.  

Price of the 1st variety of birdseed=5.68 per pound

Price of the 2nd variety of the birdseed=8.88 per pound.  

To find :

Pounds of 1st variety of birdseed are used in the mixture=?

Pounds of 2ndvariety of birdseed are used in the mixture=?

Solution:

Let the weight of 1st kind added in mixture be n pounds.

Then weight of 2nd kind will be 10 – n pounds.

Now, total cost of mixture = cost of 1st kind birdseed + cost of 2nd kind birdseed

Weight of mixture x cost per pound = weight of 1st kind x cost per pound + weight of 2nd kind x cost per pound.

Substituting the values,

$10\times8.24 = n\times5.68 + (10-n)\times8.88$

82.4 = 5.68n + 88.8 – 8.88n  

8.88n – 5.68n = 88.8 – 82.4  

3.2n = 6.4  

$n = \frac{3.2}{6.4}$

n = 2

Then, weight of 2nd kind is 10 – 2 = 8 pounds.

Hence, 2 pounds of 1st kind and 8 pounds of 2nd kind are mixed.