If you need 4 inches of pink ribbon to make a pink bow, and 2 inches of purple ribbon to make 1 bow and they have to be equal ratios. You have 120 inches of ribbon in total. How many pink bows can you make? How many purple bows can you make?

To solve this problem, let's break it down:

### Given:
- You need **4 inches of pink ribbon** for each pink bow.
- You need **2 inches of purple ribbon** for each purple bow.
- The ratio of pink bows to purple bows must remain **equal** (i.e., 1:1).
- You have a total of **120 inches** of ribbon.

### Step 1: Define Variables
Let:
- \( p \) be the number of pink bows you can make.
- \( b \) be the number of purple bows you can make.

Since the ratio of pink bows to purple bows must be equal, \( p = b \).

### Step 2: Total Ribbon Used
The total amount of ribbon used for both types of bows is:
\[
4p \, \text{(for pink bows)} + 2b \, \text{(for purple bows)} = 120 \, \text{inches}.
\]

Since \( p = b \), substitute \( b \) with \( p \):
\[
4p + 2p = 120.
\]

### Step 3: Solve for \( p \)
Combine like terms:
\[
6p = 120.
\]

Now, solve for \( p \):
\[
p = \frac{120}{6} = 20.
\]

### Step 4: Conclusion
- You can make **20 pink bows**.
- Since \( p = b \), you can also make **20 purple bows**.

### Summary:
- **20 pink bows**.
- **20 purple bows**.

Would you like more details or have any questions? 

Here are 5 questions related to this topic:
1. What happens if the ratio of pink to purple bows changes?
2. How would you adjust if you had 150 inches of ribbon instead of 120?
3. What if you need to make more purple bows than pink bows?
4. How would you calculate the ribbon needed for 10 bows of each color?
5. How could the formula change if there were multiple colors of ribbons?

**Tip:** Always set up a ratio equation first when dealing with problems involving proportional quantities.

Solve the ribbon bow problem: You need 4 inches of pink ribbon and 2 inches of purple ribbon per bow, maintaining a 1:1 ratio. With 120 inches of total ribbon, learn how to determine how many pink and purple bows you can make. This problem demonstrates algebraic concepts and linear equations, suitable for Grades 6-8.

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