12. Strawbery Summer Fhonda and Nadine beth plek strawberries in the summer but for different companies. Rhonda earns \( \$ 3 \) for each basket she ploke Nadine earns \( \$ 1 \) per basket she picks plus \( \$ 20 \) for the day a) Write an equation to represent the income that each girl earns at their job, where \( E \) is their tatal earning for one day in dollars and \( n \) is the number of baskets of strawberries picked that day. Rhonda: \( \qquad \) Nadine: \[ E=1(n)+20 \] b) If they each pick 15 baskets of strawberries, who makes more money and by how much? Show your work \[ \begin{array}{l} \text { 'r thonda: } E=3(15), E=45 \$ \\ \text { Nadine: } E=1(15)+20, E=35 \$ \end{array} \] * rhonda earns more money c) If they each earn \$81, how many baskets of strawberries does eachgin pick? Show your work. Thond: \( 81=3(n), 81 \div 3=n,(n=27 \) Nadine: \( 81=1(n)+20,81-20=61 \) so \( n=61 \) e) Determine the point of intersection algebraically by substitution or elimination.

### Problem 12: Strawberry Summer Rhonda and Nadine pick strawberries in the summer for different companies, each with their own payment structure: - **Rhonda:** Earns \$3 for each basket she picks. - **Nadine:** Earns \$1 for each basket she picks **plus** a flat \$20 for the day. Let's address each part of the problem step-by-step. --- #### **a) Writing the Income Equations** Let: - \( E \) = Total earnings for the day (in dollars) - \( n \) = Number of baskets picked in a day **Rhonda's Earnings:** \[ E = 3n \] **Nadine's Earnings:** \[ E = 1n + 20 \] \[ E = n + 20 \] --- #### **b) Comparing Earnings for 15 Baskets** If both Rhonda and Nadine pick **15 baskets**, let's calculate their earnings. **Rhonda:** \[ E = 3n \] \[ E = 3 \times 15 \] \[ E = \$45 \] **Nadine:** \[ E = n + 20 \] \[ E = 15 + 20 \] \[ E = \$35 \] **Conclusion:** Rhonda earns **more** money than Nadine when picking 15 baskets. **Difference:** \[ \$45 - \$35 = \$10 \] --- #### **c) Determining Number of Baskets for \$81 Earnings** If both Rhonda and Nadine earn **\$81** in a day, find the number of baskets each picked. **Rhonda:** \[ E = 3n \] \[ 81 = 3n \] \[ n = \frac{81}{3} \] \[ n = 27 \] **Nadine:** \[ E = n + 20 \] \[ 81 = n + 20 \] \[ n = 81 - 20 \] \[ n = 61 \] **Conclusion:** - **Rhonda** picked **27 baskets**. - **Nadine** picked **61 baskets**. --- #### **e) Finding the Point of Intersection** To determine when Rhonda and Nadine earn the **same amount**, we need to find the point where their earnings equations intersect. This means solving for \( n \) and \( E \) when both equations are equal. **Given Equations:** 1. \( E = 3n \)  (Rhonda) 2. \( E = n + 20 \) (Nadine) **Step 1: Set the Equations Equal to Each Other** \[ 3n = n + 20 \] **Step 2: Solve for \( n \)** \[ 3n - n = 20 \] \[ 2n = 20 \] \[ n = \frac{20}{2} \] \[ n = 10 \] **Step 3: Find \( E \) Using Rhonda's Equation** \[ E = 3n \] \[ E = 3 \times 10 \] \[ E = \$30 \] **Conclusion:** The **point of intersection** is at \( n = 10 \) baskets and \( E = \$30 \). **Point of Intersection:** \( (10, 30) \) --- This means that when both Rhonda and Nadine pick **10 baskets**, they each earn **\$30** for the day.