Problem 55 - Elementary Algebra

Question

Simplify. Audry bought 4 bags of marbles each containing 15 assorted marbles. If she wishes to divide them up evenly between her 3 children, how many will each child receive?

Step-by-Step Solution

Answer

Each child will receive 20 marbles.

Step 1: Calculate Total Number of Marbles

To find out the total number of marbles Audry has, multiply the number of bags by the number of marbles in each bag. The calculation is: \[ 4 \text{ bags} \times 15 \text{ marbles per bag} = 60 \text{ marbles} \]

Step 2: Distribute Marbles Evenly Among Children

Now, divide the total number of marbles by the number of children to find out how many marbles each child will receive. The calculation is: \[ \frac{60 \text{ marbles}}{3 \text{ children}} = 20 \text{ marbles per child} \]

Key Concepts

Multiplication

Multiplication is one of the fundamental arithmetic operations that helps us combine equal groups of objects. In our problem, Audry bought multiple bags of marbles, and each bag contained a set number of marbles. To find out the total number of marbles, we use multiplication.

When we multiply, we are essentially doing repeated addition. For example, if you have 4 groups and each group contains 15 items, multiplication allows you to quickly find the total number of items without adding several times. The expression for this is:

• 4 (number of bags) times 15 (marbles per bag)

This results in 60 marbles in total. This mathematical operation provides a quick and efficient way to handle large numbers and repeated sums.

Problem Solving

Problem solving is at the heart of mathematics and involves finding a way to achieve a goal when the solution is not immediately obvious. In this exercise, we approached problem solving by first understanding the question: How can Audry divide her marbles evenly among her children?

To solve this problem, we used a two-step process:

• First, calculate the total number of marbles by multiplying the quantities known (4 bags and 15 marbles each).
• Then, distribute those marbles evenly among the children using division.

By breaking the problem into smaller, more manageable parts, we can simplify the process and reach a solution. This strategy is useful beyond math and can be applied to various real-life situations.

Arithmetic Operations

Arithmetic operations are the basic building blocks for most of the calculations we perform every day. These operations include addition, subtraction, multiplication, and division. Each operation serves a different purpose.

In our exercise, we used two key operations:

• Multiplication: To find the total number of marbles, we multiplied 4 bags by 15 marbles in each bag, resulting in 60 marbles.
• Division: To split or distribute these marbles evenly among 3 children, we divided the total number of marbles by the number of children, resulting in 20 marbles for each child.

Understanding and using these operations can help solve problems effectively. Arithmetic operations also form the foundation for more advanced mathematical concepts as they build skills in calculating and reasoning.