Unit 2 Lesson 8 Cumulative Practice Problems 1. Priya is buying raisins and almonds to make trail mix. Almonds cost \( \$ 5.20 \) per pound and raisins cost \( \$ 2.75 \) per pound. Priya spent \( \$ 11.70 \) buying almonds and raisins. The relationship between pounds of almonds \( a \), pounds of raisins \( r \), and the total cost is represented by the equation \( 5.20 a+2.75 r=11.70 \). How many pounds of raisins did Priya buy if she bought the following amounts of almonds: a. 2 pounds of almonds b. 1.06 pounds of almonds c. 0.64 pounds of almonds d. a pounds of almonds

To determine how many pounds of raisins (\( r \)) Priya bought based on the amount of almonds (\( a \)) she purchased, we can use the given equation: \[ 5.20a + 2.75r = 11.70 \] **Solving for \( r \):** \[ 2.75r = 11.70 - 5.20a \] \[ r = \frac{11.70 - 5.20a}{2.75} \] Now, let's solve for each part: --- ### a. **When Priya buys 2 pounds of almonds (\( a = 2 \)):** \[ r = \frac{11.70 - 5.20 \times 2}{2.75} = \frac{11.70 - 10.40}{2.75} = \frac{1.30}{2.75} \approx 0.47 \text{ pounds} \] **Answer:** Priya bought approximately **0.47 pounds** of raisins. --- ### b. **When Priya buys 1.06 pounds of almonds (\( a = 1.06 \)):** \[ r = \frac{11.70 - 5.20 \times 1.06}{2.75} = \frac{11.70 - 5.512}{2.75} = \frac{6.188}{2.75} \approx 2.25 \text{ pounds} \] **Answer:** Priya bought approximately **2.25 pounds** of raisins. --- ### c. **When Priya buys 0.64 pounds of almonds (\( a = 0.64 \)):** \[ r = \frac{11.70 - 5.20 \times 0.64}{2.75} = \frac{11.70 - 3.328}{2.75} = \frac{8.372}{2.75} \approx 3.05 \text{ pounds} \] **Answer:** Priya bought approximately **3.05 pounds** of raisins. --- ### d. **When Priya buys \( a \) pounds of almonds:** \[ r = \frac{11.70 - 5.20a}{2.75} \] **Simplified Expression:** \[ r = \frac{11.70}{2.75} - \frac{5.20}{2.75}a \approx 4.25 - 1.89a \] **Answer:** The number of pounds of raisins is given by \[ r = \frac{11.70 - 5.20a}{2.75} \approx 4.25 - 1.89a \] --- **Summary of Results:** - **a.** 0.47 pounds - **b.** 2.25 pounds - **c.** 3.05 pounds - **d.** \( r = \frac{11.70 - 5.20a}{2.75} \) or approximately \( r = 4.25 - 1.89a \)