Problem 114 - Elementary Algebra

Question

The precipitation in inches for a particular 3 -day weekend was published as 310 inches on Friday, 112 inches on Saturday, and 34 inches on Sunday. Calculate the total precipitation over this period.

Step-by-Step Solution

Answer

The total precipitation is 456 inches.

Step 1: Understanding the Problem

We need to find the total amount of precipitation over a 3-day period (Friday to Sunday). The precipitation values given are: 310 inches on Friday, 112 inches on Saturday, and 34 inches on Sunday.

Step 2: Setting Up the Equation

To find the total precipitation, we will add the precipitation from each day together. The equation will be: \( 310 + 112 + 34 \).

Step 3: Performing the Addition

Calculate the sum of the daily precipitation values: \( 310 + 112 + 34 \). Start by adding 310 and 112 to get 422, then add 34 to 422.

Step 4: Calculating the Final Sum

Add the remaining value: \( 422 + 34 = 456 \). Thus, the total precipitation over the 3-day period is 456 inches.

Key Concepts

Step-by-step solution

When tackling a math problem, breaking it down into manageable parts can make it more digestible. This approach helps you see each action required. In the given exercise, we start by clearly understanding the task: summing up precipitation over three days. Knowing what's required is the first step in any step-by-step solution.
Next, set up the problem using an equation. By writing out what you know and what you need to find, the solution becomes more structured. For the precipitation example, list out the rainfall in inches for each day. Then express it as a sum equation:

• Friday: 310 inches
• Saturday: 112 inches
• Sunday: 34 inches
• Equation: \( 310 + 112 + 34 \)

Once the equation is set, perform the operations in parts. Adding the numbers sequentially helps avoid mistakes. Break it down:
First, add the precipitation for Friday and Saturday. Then sum this result with Sunday's precipitation value, arriving at the final total.

Algebraic problem solving

Algebraic problem-solving is a critical skill that involves translating word problems into mathematical expressions or equations. This method helps you find out what needs to be calculated and how. In this exercise, precipitation values are added together.
Algebraic thinking often involves looking for patterns, organizing information, and simplifying complex problems. With a step-by-step approach, you can identify what information is given and assign them proper numbers. Each value must be correctly represented before any math is performed.
This process generally involves establishing an equation. An equation provides a framework for solving the problem. Remember, equations in algebra don't just involve unknowns and variables; they can also simplify seemingly straightforward problems by making all required operations clear. In our example, it’s straightforward: calculate the total given specific daily values using an addition equation.

Basic arithmetic operations

Basic arithmetic operations, such as addition, are fundamental to understanding more complex mathematical concepts. They are the building blocks for different types of calculations. To solve the original problem, addition is the primary operation used.
Addition refers to combining numbers to estimate a larger whole. The process requires numerical accuracy, especially when dealing with several data points like in the precipitation example. To perform addition correctly, start from one side and move methodically to the other. It is often easier when started with the largest numbers.
For example, add 310 (Friday’s total) to 112 (Saturday’s total) to get 422 inches. Then add 34 inches (Sunday’s total) to this sum for a final result of 456 inches. Breaking addition tasks into smaller maneuvers prevents potential confusion, ensuring accuracy throughout the problem-solving process.