Problem 24 - Intermediate Algebra

Question

Translate each phrase to an algebraic expression. Answers may vary depending on the variables chosen. 100 less than triple the attendance \(a\)

Step-by-Step Solution

Answer

The algebraic expression is \(3a - 100\).

Step 1 - Understanding the Phrase

The phrase given is "100 less than triple the attendance \(a\)." First, identify the key components of the phrase: "triple the attendance \(a\)" and "100 less than".

Step 2 - Translate 'Triple the Attendance'

The phrase "triple the attendance \(a\)" means we need to multiply the attendance by 3. Therefore, the expression for this part is \(3a\).

Step 3 - Translate '100 Less Than'

The phrase "100 less than" indicates we need to subtract 100 from the expression derived in the previous step. Thus, the expression will be \(3a - 100\).

Step 4 - Construct the Algebraic Expression

Combine Step 2 and Step 3 to write the complete algebraic expression. "100 less than triple the attendance \(a\)" translates to \(3a - 100\).

Key Concepts

Understanding Algebraic Expressions

An algebraic expression is a way to represent a mathematical problem or scenario using symbols and variables. Think of it as a bridge connecting words to math. For instance, when given a phrase like "100 less than triple the attendance \(a\)," we identify what mathematical action the words represent. "Triple the attendance" points to multiplying by three, and "100 less than" tells us to subtract 100. Each piece of the phrase translates into a part of the algebraic expression, ultimately forming a complete picture of the mathematical relationship.

Variable Identification

Identifying variables is crucial in translating phrases into algebraic expressions. A variable, typically denoted by a letter such as \(a\), \(x\), or \(y\), stands in for a number we may not yet know. In our example, "attendance \(a\)," \(a\) is the variable representing the amount of attendance. Recognizing what the variable stands for in the context can simplify your math journey.

• A variable can change or have various values.
• Always choose a letter that makes sense within the context for clarity.
• Variables connect words to numbers in mathematical expressions.

Knowing your variable is like having the key to unlocking the mystery of a math problem!

Mathematical Operations in Expressions

Mathematical operations are the actions we take with numbers and variables. They are the building blocks of algebraic expressions. Let's look into the operations seen in our example:

• **Addition** involves combining values, such as \(x + y\).
• **Subtraction** means taking one value away from another. "100 less than" tells us to subtract 100, hence \(3a - 100\).
• **Multiplication** is when you combine groups of a number, like "triple" indicates multiplication by three, leading to \(3a\).
• **Division** splits a number into parts, though it isn't used in our specific example.

These operations take the basic figures from words and convert them into mathematical actions, making algebra a systematic method for problem-solving. Understanding these operations ensures you're prepared to unravel any mathematical puzzle set before you.