Problem 124 - Prealgebra

Question

Weight Seven men rented a fishing boat. The weights of the men were 175, 192, 148, 169, 205, 181, and 225 pounds. What was the total weight of the seven men?

Step-by-Step Solution

Answer

The total weight of the seven men is 1295 pounds.

Step 1 - List the weights

First, write down the weights of all seven men: 175, 192, 148, 169, 205, 181, and 225 pounds.

Step 2 - Add the weights together

Sum all the weights to find the total weight. Calculate: \[ 175 + 192 + 148 + 169 + 205 + 181 + 225 \]

Step 3 - Perform the calculation

Compute the sum: \[ 175 + 192 + 148 + 169 + 205 + 181 + 225 = 1295 \]

Key Concepts

Addition

Addition is one of the most basic arithmetic operations and it is used to combine multiple numbers into a single total. In this exercise, we need to add the weights of seven men. Addition can be done by lining up the numbers and summing them one by one. This is a straightforward process but requires attention to detail to avoid mistakes.

For example, let's add the weights provided: 175, 192, 148, 169, 205, 181, and 225. Write them down and then sum them up:

• Start with the first two numbers: 175 + 192 = 367
• Add the next number to the result: 367 + 148 = 515
• Continue this process: 515 + 169 = 684, 684 + 205 = 889, 889 + 181 = 1070, 1070 + 225 = 1295

By methodically adding each subsequent number to the running total, you'll arrive at the final sum. This is essential for ensuring accuracy and provides the correct total weight of 1295 pounds for the seven men.

Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. They form the foundation of most mathematical calculations. In this exercise, we focus on addition, which combines multiple numbers. Knowing basic arithmetic operations is crucial because they are used in everyday life for various tasks.

Arithmetic operations follow specific properties and rules. For example, addition is commutative and associative, meaning \(a + b = b + a\) and \( (a + b) + c = a + (b + c) \). To illustrate, adding the weights 175, 192, and 148 can follow:

• First grouping: \((175 + 192) + 148 = 367 + 148 = 515\)
• Second grouping: \(175 + (192 + 148) = 175 + 340 = 515\)

This flexibility allows you to perform calculations in an order that might make mental math easier.

Understanding and applying these principles help solve various arithmetic problems more efficiently.

Problem Solving

Problem-solving in math involves understanding the problem, devising a plan, carrying out the plan, and reviewing your work. For our problem of finding the total weight of seven men, we can break it down into clear steps:

• Step 1: Understand the problem. We need to find the total weight by adding up individual weights.
• Step 2: Devise a plan. List all weights and sum them.
• Step 3: Carry out the plan. Add each weight systematically as shown: 175, 192, 148, 169, 205, 181, 225.
• Step 4: Review your work. Double-check each addition step to ensure accuracy.

This structured approach helps to tackle even complex problems by breaking down into manageable parts.

Reviewing and verifying at each step ensures the final solution is correct and reduces errors. By practicing and refining these problem-solving steps, you develop stronger analytical and logical thinking skills.