Name LESSON 8.4 More Practicel Solve Two-Step Problems Homework Model with Mathematics Write two equations with letters for the unknowns. Solve. You can use a visual model to help. 1 Gemma has 3 rose bushes, each with the same number of roses. She picks 4 of the roses. There are 20 roses left on the rose bushes. How many roses were on each rose bush? $$ \qquad $$ $$ \qquad $$ 2 Brianna cuts a piece of yarn into ( 4 equal-length pieces. Then she cuts 2 inches off one of the pieces, leaving 5 inches of yarn on the piece. What was the length of the original piece of yarn? $$ \qquad $$ $$ \qquad $$ 3 Milo has 5 rocks in his rock collection. He finds 40 rocks outside that he wants to put in his collection. If he places the rocks into boxes of 9 , how many boxes of rocks will he have in his collection? $$ \qquad $$ $$ \qquad $$ 4 In the mountains, Mrs. Flores can rent a campsite for $$ \$ 9 $$ each day, plus a one-time fee of $$ \$ 25 $$. She rents a campsite for 4 days. How much does it cost Mrs. Flores to rent the campsite? $$ \qquad $$ $$ \qquad $$

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Sure, let's tackle each of these two-step problems by modeling them with mathematical equations. We'll define variables, set up equations based on the problem descriptions, and then solve them step by step.

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### **Problem 1**

**Gemma has 3 rose bushes, each with the same number of roses. She picks 4 of the roses. There are 20 roses left on the rose bushes. How many roses were on each rose bush?**

#### **Step 1: Define the Variable**
- Let **$$ x $$** represent the number of roses on each rose bush.

#### **Step 2: Set Up the Equations**
1. **Total Roses on All Bushes Initially:**
   $$
   \text{Total Roses} = 3x
   $$
2. **After Picking 4 Roses:**
   $$
   3x - 4 = 20
   $$

#### **Step 3: Solve the Equations**
$$
3x - 4 = 20 \
3x = 20 + 4 \
3x = 24 \
x = \frac{24}{3} \
x = 8
$$

#### **Answer:**
Each rose bush originally had **8 roses**.

---

### **Problem 2**

**Brianna cuts a piece of yarn into 4 equal-length pieces. Then she cuts 2 inches off one of the pieces, leaving 5 inches of yarn on the piece. What was the length of the original piece of yarn?**

#### **Step 1: Define the Variable**
- Let **$$ x $$** represent the length of each equal-length piece after the first cut.

#### **Step 2: Set Up the Equations**
1. **Original Length of the Yarn:**
   $$
   \text{Total Length} = 4x
   $$
2. **After Cutting 2 Inches Off One Piece:**
   $$
   x - 2 = 5
   $$

#### **Step 3: Solve the Equations**
$$
x - 2 = 5 \
x = 5 + 2 \
x = 7
$$
$$
\text{Total Length} = 4x = 4 \times 7 = 28 \text{ inches}
$$

#### **Answer:**
The original piece of yarn was **28 inches** long.

---

### **Problem 3**

**Milo has 5 rocks in his rock collection. He finds 40 rocks outside that he wants to put in his collection. If he places the rocks into boxes of 9, how many boxes of rocks will he have in his collection?**

#### **Step 1: Define the Variable**
- Let **$$ b $$** represent the number of boxes needed.

#### **Step 2: Set Up the Equations**
1. **Total Rocks After Finding More:**
   $$
   \text{Total Rocks} = 5 + 40 = 45
   $$
2. **Rocks per Box:**
   $$
   9b = 45
   $$

#### **Step 3: Solve the Equations**
$$
9b = 45 \
b = \frac{45}{9} \
b = 5
$$

#### **Answer:**
Milo will have **5 boxes** of rocks in his collection.

---

### **Problem 4**

**In the mountains, Mrs. Flores can rent a campsite for \$9 each day, plus a one-time fee of \$25. She rents a campsite for 4 days. How much does it cost Mrs. Flores to rent the campsite?**

#### **Step 1: Define the Variables**
- Let **$$ d $$** represent the number of days.
- Let **$$ C $$** represent the total cost.

#### **Step 2: Set Up the Equations**
1. **Daily Cost:**
   $$
   \text{Cost for Days} = 9d
   $$
2. **Total Cost Including One-Time Fee:**
   $$
   C = 9d + 25
   $$
   - Here, $$ d = 4 $$

#### **Step 3: Solve the Equations**
$$
C = 9 \times 4 + 25 \
C = 36 + 25 \
C = 61
$$

#### **Answer:**
It costs Mrs. Flores **\$61** to rent the campsite for 4 days.

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I hope this helps you understand how to model and solve two-step word problems using mathematical equations! If you have any more questions or need further clarification, feel free to ask.
**Problem 1:** - Each rose bush had **8 roses**. **Problem 2:** - The original yarn was **28 inches** long. **Problem 3:** - Milo will have **5 boxes** of rocks. **Problem 4:** - Mrs. Flores paid **\$61** to rent the campsite for 4 days.

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