Problem 62 - Algebra A Combined Function

Question

Write each algebraic expression described. The largest meteorite in the world is the Hoba West located in Namibia. Its weight is 3 times the weight of the Armanty meteorite located in Outer Mongolia. If the weight of the Armanty meteorite is \(y\) kilograms, express the weight of the Hoba West meteorite as an algebraic expression in \(y\).

Step-by-Step Solution

Answer

The weight of the Hoba West meteorite is \( 3y \) kilograms.

Step 1: Understand the Problem

We need to express the weight of the Hoba West meteorite in terms of the weight of the Armanty meteorite, which is given as \( y \) kilograms. "The weight is 3 times," indicates multiplication.

Step 2: Set Up the Expression

Given that the weight of the Hoba West meteorite is 3 times the weight of the Armanty meteorite, we multiply the weight of the Armanty meteorite by 3. The expression becomes \( 3y \).

Step 3: Finalize the Algebraic Expression

The expression for the weight of the Hoba West meteorite in terms of the weight of the Armanty meteorite is \( 3y \).

Key Concepts

Multiplication in Algebra

When dealing with algebraic expressions, multiplication is a fundamental operation. In algebra, multiplication of an unknown variable by a number is straightforward. You simply multiply the number by the variable ex. - Multiplying 3 by the variable If you have a variable like \( y \) representing a quantity, and you need to multiply it by 3, the result is expressed simply as \( 3y \).- The number and the variable are written next to each other, with the numeral first, denoting multiplication.This compactness is unique to algebra, allowing you to easily manipulate these expressions with basic arithmetic rules. Algebraic multiplication enables you to represent relationships and scaling between different quantities efficiently.

Writing Expressions

Writing expressions is a key skill in algebra that involves translating real-world situations into mathematical language. To write an algebraic expression:- Identify variables that stand for unknown or variable quantities. In our example, \( y \) is the variable for the weight of the Armanty meteorite. The task is to write this in terms of something else.- Recognize the operations that connect these quantities. "3 times the weight" suggests multiplication. Thus, you write \( 3y \) to represent the weight of the Hoba West meteorite.This skill is not just about numbers and operations; it’s about communicating real-world problems mathematically. Expressions act as a bridge, offering a simplified view of complex problems.

Algebraic Problem Solving

Algebraic problem solving allows you to address and solve different mathematical tasks by relying on expressions. Here's the general strategy:- Understand the problem and identify what is being asked. In our scenario, we calculated the weight of one meteorite based on another's.- Set up the expression using known quantities and appropriate operations. Choosing the operation (in this case, multiplication by 3) is critical. It requires analyzing how quantities relate (3 times heavier).- Lastly, solve or simplify the expression for practical use or further analysis. The weight of the Hoba West meteorite is expressed as \( 3y \). This expression helps in comparing weights or solving additional problems involving these meteorites.Such systematic approaches in algebra simplify complexities and allow mathematical exploration in various real-world contexts. Algebraic problem solving is powerful as it turns descriptive problems into manageable numerical forms.