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Answer:
Let's denote the pounds of birdseed as \( x \) and the pounds of sunflower seeds as \( y \). We need to set up and solve a system of equations based on the given information.
First, the total weight of the mixture is 40 pounds:
\[
x + y = 40
\]
Second, the total cost equation for the mixture, which should average $0.76 per pound, can be set up as:
\[
0.58x + 0.88y = 0.76 \times 40
\]
Simplify the second equation:
\[
0.58x + 0.88y = 30.4
\]
We now have the system of equations:
1. \( x + y = 40 \)
2. \( 0.58x + 0.88y = 30.4 \)
Solve the first equation for \( y \):
\[
y = 40 - x
\]
Substitute this into the second equation:
\[
0.58x + 0.88(40 - x) = 30.4
\]
Distribute the \( 0.88 \):
\[
0.58x + 35.2 - 0.88x = 30.4
\]
Combine like terms:
\[
-0.30x + 35.2 = 30.4
\]
Subtract 35.2 from both sides:
\[
-0.30x = -4.8
\]
Solve for \( x \):
\[
x = \frac{-4.8}{-0.30} = 16
\]
So, Angela should use 16 pounds of birdseed.
Now, find \( y \):
\[
y = 40 - x = 40 - 16 = 24
\]
Angela should use 16 pounds of birdseed and 24 pounds of sunflower seeds.
To verify, let's check the cost:
\[
0.58 \times 16 + 0.88 \times 24 = 9.28 + 21.12 = 30.4
\]
Thus, the calculations are correct. The simplified