Question

Mr. White's math class has \(n\) students. Mrs. Black's math class has 22 students fewer than triple the number of students in Mr. White's class. Which expression shows the number of students in Mrs. Black's class in terms of \(n\) ? (A) \(22<3 n\) (B) \(3(n-22)\) (C) \(22-3 n\) (D) \(3 n-22\)

Short answer

(D) \(3n - 22\)

Step-by-step solution

Translate the Problem into an Expression

We are given that Mrs. Black's class has 22 students fewer than triple the number of students in Mr. White's class. Let's use these words to create an expression. "Triple the number of students in Mr. White's class" could be written as \(3n\). "22 students fewer than" means we need to subtract 22 from that value, so the expression would be \(3n - 22\). This expression represents the number of students in Mrs. Black's class.

Identify the Matching Option

Now that we have the expression \(3n - 22\), let's find the matching option among the given choices: (A) \(22<3n\) (B) \(3(n-22)\) (C) \(22-3n\) (D) \(3n-22\) The expression \(3n - 22\) matches with option (D), so the correct answer is: (D) \(3n - 22\)

Key concepts

Math Word Problems

Deciphering math word problems can often seem like a daunting task, but it's a critical skill that is frequently tested on, especially in exams like the GED. When approaching a word problem, the goal is to translate the given information into an algebraic expression or equation.

Take the example from the math class problem: the task is to represent Mrs. Black's class size in relation to Mr. White's class size, described in words. The key steps are identifying the numerical relationships and the operations those words represent. Phrases like 'triple the number of students' point to multiplication, while '22 students fewer' indicates subtraction.

In practice, it's helpful to underline or highlight keywords and numbers that will form the parts of your algebraic sentence. This method ensures that all relevant pieces of information are considered when constructing the expression and nothing is overlooked. Always look for clue words that signal specific operations, and writing out an intermediate word equation can be a useful intermediate step before jumping to the symbols of algebra.

GED Math Practice

Preparing for the General Educational Development (GED) test, specifically the math portion, requires familiarity with a range of concepts, from basic arithmetic to more complex algebraic expressions. It's key for students to develop strong problem-solving strategies.

One such strategy is understanding how to break down word problems into manageable parts. As illustrated with the classroom word problem, identifying what you're solving for – in this case, the number of students in Mrs. Black's class – and what information you've been given are the first essential steps.

GED math practice involves not just rote memorization of formulas, but also sharpening the ability to interpret and set up word problems. A variety of practice problems, covering topics such as algebra, geometry, and data analysis, can build the necessary skills to excel on the test. It’s also advisable to time practice sessions to get used to the pace you’ll need to maintain during the actual exam.

Expressing Relationships in Algebra

Expressing relationships in algebra involves creating equations or expressions that accurately represent the connections between different quantities. An understanding of variables, coefficients, and standard mathematical operations is essential here.

In the classroom problem, the relationship is between the number of students in two classes. Algebra allows us to represent Mrs. Black's class size in terms of Mr. White's class size with a variable, 'n'. We express '22 students fewer than three times' as an algebraic expression by recognizing that 'three times' corresponds to multiplication and 'fewer than' to subtraction, leading us to the expression '3n - 22'.

These algebraic expressions are the foundation for solving problems and can later be manipulated to help us find specific values or compare relationships. Building fluency with variables and operations, and practicing how they interplay within expressions, is a cornerstone of algebraic thinking and a skill that pays dividends across all areas of mathematics.