Cost of walnuts + Cost of almonds \( = \) Total Cost \[ 2 w+4 a=44 \] Number of \( +\begin{array}{c}\text { Number of }\end{array} \) pounds of walnuts \( =\begin{array}{l}\text { Total weight } \\ \text { pounds of almonds the order }\end{array} \) \( w+a \)

It looks like you're working on a system of equations to determine the number of pounds of walnuts (\(w\)) and almonds (\(a\)) based on their costs and total cost. Let's break down the information you provided and see how to set up and solve the system. ### Given: 1. **Cost Equation:** \[ 2w + 4a = 44 \] - **Interpretation:** Walnuts cost \$2 per pound, almonds cost \$4 per pound, and the total cost is \$44. 2. **Weight Equation:** \[ w + a = \text{Total Weight} \] - **Interpretation:** The total weight of walnuts and almonds combined is the sum of their individual weights. ### Missing Information: To solve for both \(w\) and \(a\), we need two independent equations. You've provided the cost equation, but the weight equation requires knowing the **total weight** of the order. Without this second piece of information, we cannot find unique values for \(w\) and \(a\). ### Assuming a Total Weight: If, for example, the **total weight** of the order is provided (let's say it's \(T\) pounds), the weight equation becomes: \[ w + a = T \] With this assumption, you can solve the system as follows: 1. **Rewrite the Weight Equation:** \[ w = T - a \] 2. **Substitute into the Cost Equation:** \[ 2(T - a) + 4a = 44 \] \[ 2T - 2a + 4a = 44 \] \[ 2T + 2a = 44 \] \[ 2a = 44 - 2T \] \[ a = 22 - T \] 3. **Find \(w\):** \[ w = T - a = T - (22 - T) = 2T - 22 \] ### Example: Let's assume the **total weight** \(T\) is **12 pounds**. 1. **Find \(a\):** \[ a = 22 - 12 = 10 \text{ pounds of almonds} \] 2. **Find \(w\):** \[ w = 12 - 10 = 2 \text{ pounds of walnuts} \] 3. **Verification:** \[ 2w + 4a = 2(2) + 4(10) = 4 + 40 = 44 \text{ dollars} \] The numbers satisfy the cost equation. ### Conclusion: To determine the exact number of pounds of walnuts and almonds, **you need to know the total weight** of the order. Once you have that, you can substitute it into the weight equation and solve the system of equations as illustrated above. If you provide the total weight, I'd be happy to help you solve the equations with that specific value!