Problem 59 - Elementary Algebra Within Reach

Question

In Exercises 57-60, write an algebraic expression for the statement. $$ \text { The cost of } m \text { pounds of meat when the cost per pound is } \$ 3.79 $$

Step-by-Step Solution

Answer

The algebraic expression representing the cost of \(m\) pounds of meat when the cost per pound is $3.79 is \(3.79m\).

Step 1: Identify the Variables

From the problem, we can identify two variables. One is the quantity of meat bought denoted as \(m\) pounds, and the second variable is the cost per pound which is given as $3.79.

Step 2: Formulate the Problem into an Algebraic Expression

Using these variables, we can write the total cost for \(m\) pounds of meat as the product of the number of pounds bought and the price per pound. So, the cost for \(m\) pounds of meat when the cost per pound is $3.79 can be written as \(3.79m\).

Key Concepts

Variables in Algebra

When we come across algebra, it's like meeting the backbone of mathematics that involves letters and symbols representing numbers and quantities. These symbols or letters are called variables, and they are foundational elements in algebraic expressions.

Think of variables as containers or placeholders that can hold various values. In the context of our exercise, we're looking at the variable m, which represents the pounds of meat. You can imagine m as a flexible number that we can adjust based on how much meat we're buying. In algebra, variables allow us to write general formulas that can be applied to many different situations, just like the one in the exercise, without having to rewrite the entire expression each time.

Formulating Algebraic Expressions

Formulating algebraic expressions is akin to translating a spoken language into a mathematical language. It's about taking real-world situations and describing them using mathematical symbols and operations. To craft an algebraic expression, you generally start by identifying the key quantities involved and then determine how they interact with each other mathematically.

In the exercise provided, we need to articulate the total cost of buying meat as an algebraic expression. We know that the cost depends on two things: the number of pounds of meat you buy and the price per pound. These are our variables. With this information, we can write an expression, 3.79m, where m is multiplied by 3.79 to represent the overall cost. This translation from a verbal statement to an algebraic one is a skill that lies at the heart of algebra.

Cost Calculation in Algebra

Calculating cost in algebra is a practical application of algebraic expressions that we encounter often in life, especially in anything involving finance. It often involves a multiplication operation, since cost is typically a function of the quantity of items and the price per item.

In our exercise, the total cost is calculated by multiplying the number of pounds of meat by the cost per pound. The expression 3.79m encapsulates this relationship. It's worth mentioning that algebra not only makes it easy to compute the cost for one scenario but also makes it possible to quickly adjust the calculation if, for example, the price per pound or the amount of meat changes. This dynamic nature of algebra is what makes it an indispensable tool in fields that involve cost analysis and budget planning.