Mr. Moretti is making welcome bags to give to the 18 students in his homeroom on the first day of school. He puts 3 mechanical pencils in each bag. He puts twice as many regular pencils in each bag. What is the total number of pencils that Mr. Moretti gives to his students?
The correct answer and explanation is:
Let’s break down the problem step-by-step and then find the total number of pencils Mr. Moretti gives out.
Step 1: Identify the number of students
Mr. Moretti has 18 students in his homeroom.
Step 2: Number of mechanical pencils per bag
Each student receives a welcome bag with 3 mechanical pencils.
Step 3: Number of regular pencils per bag
Mr. Moretti puts twice as many regular pencils as mechanical pencils in each bag.
- Since each bag has 3 mechanical pencils,
- Number of regular pencils per bag = 2 × 3 = 6 regular pencils.
Step 4: Total pencils per bag
- Mechanical pencils per bag = 3
- Regular pencils per bag = 6
- Total pencils per bag = 3 + 6 = 9 pencils
Step 5: Total pencils for all students
- There are 18 students,
- Each gets 9 pencils,
- Total pencils = 18 × 9 = 162 pencils
Final Answer:
Mr. Moretti gives out a total of 162 pencils to his students.
Explanation:
This problem involves multiplication and understanding ratios. The key point is recognizing that the number of regular pencils is twice the number of mechanical pencils in each welcome bag. Since mechanical pencils are fixed at 3 per bag, regular pencils become 6 per bag.
By adding mechanical and regular pencils per bag, we get 9 pencils per student. Then, since there are 18 students, multiplying the pencils per bag by the number of students gives the total pencils needed.
This kind of problem is a typical example of proportional reasoning and multiplication used in everyday situations—perfect for applying basic math skills to solve real-world problems efficiently.
If Mr. Moretti had to prepare these bags, knowing the total count helps him purchase the correct quantity of pencils, avoiding shortages or excess. It also illustrates how multiplication is used not just for simple calculations but to handle quantities that scale with the number of people or items involved.