The Brittle Bird Store prepares bird-seed blends by mixing sunflower seeds and millet and packaging them in 5 -pound bags te sale. Sunflower seed $$ (s) $$ is regularly sold for $$ \$ 1.75 $$ per pound, and millet $$ (m) $$ is sold for $$ \$ 2.50 $$ per pound. The minure is soh for $$ \$ 11.60 $$. Which system of equations can be used to find the number of pounds of each type of seed in the mimure?

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To determine the number of pounds of sunflower seeds ($$ s $$) and millet ($$ m $$) in the 5-pound bird-seed blend, we can set up a system of two equations based on the given information:

1. **Total Weight Equation:**
   
   The total weight of the blend is 5 pounds. Therefore:
   $$
   s + m = 5
   $$

2. **Total Cost Equation:**
   
   The cost of sunflower seeds is \$1.75 per pound, and the cost of millet is \$2.50 per pound. The total cost of the blend is \$11.60. Therefore:
   $$
   1.75s + 2.50m = 11.60
   $$

**System of Equations:**
$$
\begin{cases}
s + m = 5 \
1.75s + 2.50m = 11.60
\end{cases}
$$

This system can be used to solve for the values of $$ s $$ and $$ m $$, representing the pounds of sunflower seeds and millet in the mixture, respectively.

**Example Solution:**

1. From the first equation, solve for $$ s $$:
   $$
   s = 5 - m
   $$

2. Substitute $$ s = 5 - m $$ into the second equation:
   $$
   1.75(5 - m) + 2.50m = 11.60
   $$
   $$
   8.75 - 1.75m + 2.50m = 11.60
   $$
   $$
   0.75m = 2.85
   $$
   $$
   m = 3.8 \text{ pounds}
   $$

3. Substitute $$ m = 3.8 $$ back into $$ s = 5 - m $$:
   $$
   s = 5 - 3.8 = 1.2 \text{ pounds}
   $$

So, the blend consists of **1.2 pounds of sunflower seeds** and **3.8 pounds of millet**.

**Answer:**  
One equation states s + m = 5 and the other 1.75 s + 2.50 m = 11.60. Thus,

s + m = 5  
 1.75s + 2.50m = 11.60
To find the number of pounds of sunflower seeds ($$ s $$) and millet ($$ m $$) in the 5-pound bird-seed blend, use the following system of equations: 1. $$ s + m = 5 $$ 2. $$ 1.75s + 2.50m = 11.60 $$ This system allows you to determine the exact amounts of each seed type in the mixture.

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