Problem 58 - Elementary Algebra Within Reach

Question

In Exercises 57-60, write an algebraic expression for the statement. The cost for a family of \(n\) people to see a movie when the cost per person is \(\$ 8.25\)

Step-by-Step Solution

Answer

The algebraic expression that represents the cost for a family of \(n\) people seeing a movie at the rate of $8.25 per person is \(Cost = \$8.25 \times n\).

Step 1: Write down the given values

We have two values: the cost per person which is $8.25 and number of people, represented as \(n\).

Step 2: Formulate the algebraic expression

In order to find out the total cost for \(n\) people, we will need to multiply the cost per person by the number of people. This can be represented in an algebraic expression as \(Cost = \$8.25 \times n\).\n

Key Concepts

Cost Calculation

When it comes to cost calculation, understanding how to translate a situation into a mathematical expression is essential. Cost calculation refers to determining the total amount needed for a particular service or product.
In this exercise, our task is to calculate the total cost for a family to attend a movie. Since the price per person is given as \(8.25, and the family consists of \(n\) people, we need to compute how much it will cost altogether.
To do this, think of each individual as contributing to the overall expense, and since the amount each pays is constant (\)8.25 here), this directly influences the total based on how many people are involved.

Basic Algebra

Basic algebra involves manipulating variables and constants to form mathematical expressions or solve equations. It's about understanding how numbers and placeholders (like \(n\)) interact.
In this exercise, we have two key components: a constant cost per person, which is $8.25, and a variable \(n\), which represents the number of people in the family.
Through basic algebra, we recognize that to find the total cost, these two components must be related through an operation (in this case, multiplication).
This process demonstrates the power of algebra: taking verbal statements and turning them into expressions that can be easily calculated and used.

Multiplication

Multiplication is one of the foundational operations in mathematics, often symbolized by \(\times\). It allows us to combine equal groups efficiently.
In the context of this problem, multiplication helps us determine the total cost seamlessly. The mathematical representation \(Cost = 8.25 \times n\) illustrates this.
Here, multiplication is used to find out the total expense by scaling the known cost per person up by the number of people. It replaces repeated addition, making calculations quicker and neater.

• Consider $8.25 as a single unit of cost.
• Multiply this by \(n\), the quantity of units (people).
• Resulting in a swift computation of combined cost.

Thus, multiplication turns the input values into a straightforward total cost figure.