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.

Question

UpStudy AI · Accepted Answer

### 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.
**a) Income Equations:** - **Rhonda:** $$ E = 3n $$ - **Nadine:** $$ E = n + 20 $$ **b) Earnings for 15 Baskets:** - **Rhonda:** \$45 - **Nadine:** \$35 - **Rhonda earns more by \$10.** **c) Number of Baskets for \$81:** - **Rhonda:** 27 baskets - **Nadine:** 61 baskets **e) Point of Intersection:** - Both earn \$30 when picking 10 baskets.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Algebra Questions