Problem 16 The number of fans produced by a... [FREE SOLUTION] (2024)

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Inequalities are mathematical expressions that show the relationship of one value being greater than, less than, or equal to another value. In this problem, the manufacturer’s production of fans and lamps is connected through an inequality. The statement mentions that the number of fans (F) produced in a week can be no more than five times the number of lamps (L). This translates to the inequality:

\[ F \leq 5L \]

By inserting the given number of fans, 20, into the inequality, we get: \[ 20 \leq 5L \]

This inequality helps us find the range of possible values for the number of lamps produced (L). Solving this inequality reveals the minimum number of lamps needed to satisfy the condition.

Solving problems involving inequalities follows a systematic approach. Here’s a step-by-step guide:

• Understand the problem: Carefully read the problem and identify what’s given and what needs to be found. In this example, we need to find the minimum number of lamps produced given the production constraints.
• Set up the inequality: Express the relationship using an inequality. Here, it’s \[20 \leq 5L \].
• Solve the inequality: Manipulate the inequality algebraically to isolate the variable. In this case, dividing both sides by 5 gives \[ 4 \leq L \].
• Interpret the solution: Understand what the solved inequality means. It shows that the number of lamps must be at least 4.

Following these steps can make solving similar problems easier and quicker.

Mathematical reasoning is crucial for solving inequalities and similar problems. It involves logical thinking and the ability to analyze given information.

Consider these aspects:

• Identify Constraints: Know the limitations or restrictions within the problem. Here, the constraint is that the number of fans cannot exceed five times the number of lamps.
• Logical Steps: Carry out operations logically and ensure each step flows from the previous one. Dividing the inequality by 5 is a logical step because it simplifies the problem.
• Double-Check: Reviewing the solution helps confirm its accuracy. By substituting L = 4 back into the inequality, we verify the solution.

Using strong mathematical reasoning ensures that the problem is approached methodically and solved correctly.

Preparing for the GED math test involves practicing various types of problems, including those involving inequalities. You can follow these tips:

• Practice Regularly: Frequent practice helps solidify understanding and improve speed. Work through a variety of inequality problems to build confidence.
• Understand Concepts: Make sure to grasp the underlying concepts rather than memorize processes. Knowing why you manipulate an inequality in a certain way is key.
• Use Resources: Take advantage of GED prep books, online resources, and practice tests. These materials often provide step-by-step solutions and explanations.
• Seek Help: If certain problems or concepts are challenging, don’t hesitate to ask for help from teachers, tutors, or study groups.

Consistent and focused preparation will improve your mathematical reasoning skills and boost your confidence on test day.