Ethan bought 4 packages of pencils. After he gave 8 pencils to his friends, he had 40 pencils.
The correct answer and explanation is:
✅ Correct Answer:
Each package contains 12 pencils.
🧠 Step-by-Step Explanation:
Let’s break down the problem logically and mathematically.
✏️ Given:
- Ethan bought 4 packages of pencils.
- He gave away 8 pencils to his friends.
- After giving them away, he had 40 pencils left.
We are asked to find out how many pencils were in each package.
🔍 Step 1: Represent the total number of pencils before giving any away.
Let’s say each package contains x pencils.
Since he bought 4 packages, the total number of pencils he had at the beginning is: 4x pencils4x \text{ pencils}
🔍 Step 2: Subtract the pencils he gave away.
Ethan gave away 8 pencils, so: Remaining pencils=4x−8\text{Remaining pencils} = 4x – 8
We are told he had 40 pencils left, so: 4x−8=404x – 8 = 40
🔍 Step 3: Solve the equation.
4x−8=404x – 8 = 40
Add 8 to both sides: 4x=484x = 48
Divide both sides by 4: x=12x = 12
🎉 Final Answer:
Each package had 12 pencils.
📘 Summary:
This type of problem helps build algebraic thinking. By setting up an equation using a variable for the unknown (pencils per package), you can solve step by step. It’s a classic example of using linear equations to model real-life problems. Ethan’s initial total of pencils (4 packages) minus the ones he gave away must equal the number he has left. This is a common approach in both school word problems and daily decision-making tasks.