Askiitians Tutor Team
Last Activity: 9 Days ago
To tackle the question from the 2018 KEAM exam, we first need to understand the context and the specific problem being presented. Typically, such questions involve forming equations based on given conditions or relationships. Let's break down the process of forming two equations step by step, using a hypothetical scenario to illustrate the concept.
Understanding the Problem
Imagine a scenario where you have two variables, say \( x \) and \( y \), representing two quantities. The question might provide certain relationships between these quantities, such as their sum, difference, or a ratio. The key is to extract these relationships clearly from the problem statement.
Identifying Relationships
Start by carefully reading the question to identify what is being asked. Look for keywords that indicate relationships:
- Sum: If the question states that the sum of two quantities is a certain value, you can write an equation like \( x + y = S \).
- Difference: If it mentions the difference, you might form an equation like \( x - y = D \).
- Product or Ratio: For products or ratios, you could have equations like \( xy = P \) or \( \frac{x}{y} = R \).
Formulating the Equations
Once you identify the relationships, you can start forming your equations. Let’s say the problem states:
- The sum of two numbers is 30.
- The difference between the two numbers is 10.
From this, you can derive the following equations:
- Equation 1: \( x + y = 30 \)
- Equation 2: \( x - y = 10 \)
Solving the Equations
With your two equations established, the next step is to solve them simultaneously. You can use methods such as substitution or elimination. For our example:
From Equation 1, you can express \( y \) in terms of \( x \):
y = 30 - x
Now, substitute this expression for \( y \) into Equation 2:
x - (30 - x) = 10
Simplifying this gives:
2x - 30 = 10
From here, you can solve for \( x \) and subsequently find \( y \).
Example Solution
Continuing from our simplification:
2x = 40
x = 20
Now substitute \( x \) back into the equation for \( y \):
y = 30 - 20 = 10
Thus, the two numbers are 20 and 10.
Final Thoughts
Forming equations from a word problem is a skill that improves with practice. Always look for the relationships between the quantities involved, and translate those relationships into mathematical expressions. With time, you’ll find that this process becomes more intuitive, allowing you to tackle even more complex problems with confidence.