Kelly had a total of 60 pens and pencils. After giving away 3/4 pens and 20 pencils, she had an equal number of pens and pencils. How many pencils did she have at first?

Let's solve this problem step by step.

### Step 1: Define Variables
Let:
- \( p \) be the number of pens Kelly initially had.
- \( c \) be the number of pencils Kelly initially had.

### Step 2: Set Up Equations Based on Given Information
1. **Total number of pens and pencils:**
   \[
   p + c = 60
   \]
2. **After giving away 3/4 of the pens and 20 pencils:**
   - The number of pens left: \( p - \frac{3}{4}p = \frac{1}{4}p \).
   - The number of pencils left: \( c - 20 \).
   
   Since the number of pens and pencils left is equal:
   \[
   \frac{1}{4}p = c - 20
   \]

### Step 3: Solve the Equations
We now have two equations:
1. \( p + c = 60 \)
2. \( \frac{1}{4}p = c - 20 \)

#### Solving the Second Equation:
Multiply both sides of the second equation by 4 to eliminate the fraction:
\[
p = 4(c - 20)
\]
\[
p = 4c - 80
\]

#### Substitute \( p \) in the First Equation:
Substitute \( p = 4c - 80 \) into \( p + c = 60 \):
\[
4c - 80 + c = 60
\]
\[
5c - 80 = 60
\]
\[
5c = 140
\]
\[
c = 28
\]

### Step 4: Find \( p \)
Substitute \( c = 28 \) back into the equation \( p + c = 60 \):
\[
p + 28 = 60
\]
\[
p = 32
\]

### Step 5: Conclusion
Kelly initially had \( \boxed{28} \) pencils.

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Would you like more details, or do you have any questions about the solution? 

Here are some related problems for practice:
1. If Kelly had 80 items and the same condition applied, how many pens and pencils did she have?
2. What if Kelly had given away 2/3 of her pens instead of 3/4?
3. Suppose Kelly had 40 pens and 60 pencils. How would the solution change?
4. How would the scenario change if Kelly gave away 20% of her pens instead of 3/4?
5. Can you create a similar problem but with markers and erasers instead of pens and pencils?
6. If Kelly initially had 50 pens, how many pencils would she have if the total remained 60?
7. What if Kelly gave away 1/2 of her pens and 15 pencils instead?
8. What would be the solution if Kelly had 100 items total?

**Tip:** Always start by defining variables and setting up equations based on the given conditions to methodically solve word problems.

Learn how to solve Kelly's problem involving pencils and pens. Kelly initially had 60 items total, including pens and pencils. After giving away 3/4 of the pens and 20 pencils, she had an equal number of pens and pencils remaining. Discover the solution step-by-step with detailed equations and calculations. Suitable for students in Grades 6-8.

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