Setting Up Equations

 

Setting Up Equations

 

Setting up equations provides an effective and practical method for solving many problems we encounter in daily life. In this study, we will learn to recognize different types of problems, work through plenty of examples, and find opportunities to improve our skills. The following topics will help reinforce equation-building skills from various angles:

  • Four Operations Problems: Based on addition, subtraction, multiplication, and division, examples that can be encountered in many areas of daily life are examined.
  • Age Problems: Practical solutions are generated with problems built on age relationships between people at different ages and stages of life, and their changes over time.
  • Worker – Pool Problems: Time calculations are made for components working at different speeds, considering processes such as completing a job or filling and emptying a pool.
  • Motion Problems: Situations that may be encountered in realistic scenarios such as travel and transportation are addressed through connections between distance, speed, and time.
  • Percentage Problems: Different applications of the concept of percentage in topics like discounts, price hikes, profit, mixtures, and interest are explained, emphasizing their areas of use in daily life.

All these topics will allow you to learn the fundamental principles of setting up equations through practical application. By solving plenty of questions, it is aimed to firmly reinforce the topics and strengthen the mathematical thinking skills needed in daily life.

 

Setting Up Equations

 

Expressing a given problem with mathematical statements is called setting up an equation. When setting up an equation, different symbols are used for each of the various unknowns we encounter. A given problem is written in the form of an equation by establishing relationships between unknowns, which are also symbolized with mathematical signs such as \( +, \; -,\; \times, \; :, \; <,\; >,\; \le,\; \ge \; \).

 

Examples:

 

\( \bullet \quad \) 7 more than a number \( \Rightarrow x+ 7 \)

\( \bullet \quad \) 3 less than a number \( \Rightarrow x- 3 \)

\( \bullet \quad \) 5 times a number \( \Rightarrow x \cdot 5 \)

\( \bullet \quad \) \( \frac{3}{7} \) of a number \( \Rightarrow x \cdot \large \frac{3}{7} \)

\( \bullet \quad \) 2 times 11 more than a number \( \Rightarrow (x+ 11 ) \cdot 2 \)

\( \bullet \quad \) \( \large \frac{4}{9} \) of 1 less than a number \( \Rightarrow (x-1 ) \cdot \large \frac{4}{9} \)

\( \bullet \quad \) 5 more than half of 3 less than a number \( \Rightarrow \large \frac{x-3}{2} + 5 \)

\( \bullet \quad \) If \( \large \frac{1}{5} \) of 2 less than 3 times a number is 10 \( \Rightarrow \large \frac{3