Answer: she should use 13 pounds of birdseed and 27 pounds of sunflower seeds.
Explanation:
Let x represent the number of pounds of birdseed that she should use.
Let y represent the number of pounds of sunflower seeds that she should use.
Angela Leinenbachs' pet store wishes to make a 40-pound mixture of birdseed and sunflower seeds. It means that
x + y = 40
Birdseed costs $0.52 a pound and sunflower seeds cost $0.82 a pound. If the mixture would sell for $0.72 per a pound, then the total cost of the mixture would be 0.72 × 40 = $28.8
The equation would be
0.52x + 0.82y = 28.8- - - - - - - - - -1
Substituting x = 40 - y into equation 1, it becomes
0.52(40 - y) + 0.82y = 28.8
20.8 - 0.52y + 0.82y = 28.8
- 0.52y + 0.82y = 28.8 - 20.8
0.3y = 8
y = 8/0.3 = 27
x + y = 40
x + 27 = 40
x = 40 - 27
x = 13