Birdseed costs $0.690.69 a pound and sunflower seeds cost $0.990.99 a pound. Angela Leinenbachs' pet store wishes to make a 5050 pound mixture of birdseed and sunflower seeds that sells for $0.810.81 per pound. How many pounds of each type of seed should she use?

30 pounds of Birdseed seed should be used and 20 pounds of Sunflower seeds should be used to make a 50 pound mixture that costs $0.81081 per pound.

Explanation:

50 pound mixture

(0.69069)(50-x)   + (0.99099)x         = 0.810.81 *50

34.5345 -0.69069x + 0.99099x = 40.54

0.300x = 40.54 - 34.534

x = 6.004 / 0.300

x = 20

50 - x = 30

30 pounds of bird seeds and 20 pounds of sunflower seeds is needed for the 50 pound mixture

Explanation:

Let us use "a" to represent the amount of bird seeds (in pounds) that will be needed for the mixture and "b" to represent the amount of sunflower seeds (in pounds) that Will also be required for the mixture.

Since bird seeds cost $0.69 per pound, sunflower seeds cost $0.99 per pound and the 50 pound mixture will be sold for $0.81 per pound (meaning that the 50 pound mixture will cost: 0.81 × 50 = $40.5).

Then : (0.69×a)+(0.99×b)= 0.81×50

0.69a+0.99b =40.5 ---this is equation 1

Since a combination of some quantities of bird seeds (in pounds) and sunflower seeds (in pounds) will be required to produce the 50 pound mixture, then:

a + b = 50 this is equation 2

From the equation above, making "b" the subject of the formula, we have:

b = 50 - a

Substitute "b" for "50 - a" in equation 1:

0.69a + [0.99×(50-a)] = 40.5

0.69a + (49.5 - 0.99a) = 40.5

0.69a + 49.5 - 0.99a = 40.5

49.5 - 0.3a = 40.5

0.3a = 49.5 - 40.5

0.3a = 9

a = 9/0.3

a = 30 pounds

Then substitute "a" for 30 in eqn 2

Substitute "a" for 30 in equation 2

30 + b = 50

b = 50 - 30

b = 20 pounds

Therefore 30 pounds of bird seeds and 20 pounds of sunflower seeds will be required to produce the 50 pound mixture that will be sold for $0.81 per pound.