Problem 331 - Prealgebra

Question

In the following exercises, solve. Government The United States Senate has twice as many senators as there are states in the United States. There are 50 states. How many senators are there in the United States Senate?

Step-by-Step Solution

Answer

There are 100 senators.

Step 1: Identify the number of states

The United States has 50 states. This will be used to calculate the number of senators.

Step 2: Set up the relationship

According to the problem, the number of senators is twice the number of states.

Step 3: Write the mathematical expression

Let the number of states be represented by 50. Then the number of senators can be represented as: \[ \text{Number of senators} = 2 \times \text{Number of states} \]

Step 4: Perform the calculation

Compute the number of senators: \[ \text{Number of senators} = 2 \times 50 = 100 \]

Step 5: Verify the result

The calculated number of senators is 100, which is double the number of states, satisfying the given condition.

Key Concepts

Basic Arithmetic Operations

Arithmetic operations are fundamental to solving mathematical problems, especially in prealgebra. They include addition, subtraction, multiplication, and division. In the given problem, we use multiplication to find the number of senators in the United States Senate. It's straightforward: we multiply the number of states by 2. For example, with 50 states and the operation being multiplication (twice the number), our expression is: \(2 \times 50\). This is an example of using a basic arithmetic operation to solve a real-world problem.

Understanding Relationships in Word Problems

Grasping the relationships described in word problems is key to solving them. In our exercise, the relationship is that the number of senators is twice the number of states. Words like 'twice' or 'double' indicate specific mathematical operations. To identify relationships:

• Read the problem carefully.
• Look for key phrases that indicate operations.
• Understand how different quantities relate to each other.

In this problem, the phrase 'twice as many' signals that multiplication is the required operation, specifically doubling the number of states to find the number of senators.

Convert Word Problems to Mathematical Expressions

Turning words into math expressions is an essential skill. Let’s break down the process with the given problem:

• Identify the known quantities and representations. Here, the number of states is 50.
• Determine the mathematical operation. The problem states 'twice as many,' meaning we will multiply by 2.
• Write the mathematical expression. If the number of states is 50, then \(2 \times 50\) will give the number of senators.

Practicing these steps helps you convert any word problem into a mathematical expression, which is crucial for solving real-world math problems.