Question

In a class test, Veer scored 6 more than twice as many marks as Kevin scored. If one of them had scored 4 more marks, their total score would have been 40. Find the marks obtained by Veer and Kevin.

Hint:

Always check your final answers against the original word problem. Twice Kevin's marks (20) plus 6 is 26 (Veer's marks). Their sum (36) plus 4 is 40. The logic holds!

Answer 1

Step 1: Understanding the Concept:
Translate the given word problem into linear equations.
Step 2: Key Formula or Approach:
Let the marks obtained by Kevin be \(x\) and marks obtained by Veer be \(y\).
Step 3: Detailed Explanation:
From the first condition: Veer scored 6 more than twice Kevin's marks.
\[ y = 2x + 6 \quad \text{--- (i)} \]
From the second condition: If one of them scored 4 more marks, total is 40.
If Kevin scored 4 more: \((x + 4) + y = 40 \Rightarrow x + y = 36\).
If Veer scored 4 more: \(x + (y + 4) = 40 \Rightarrow x + y = 36\).
In either case, the equation is:
\[ x + y = 36 \quad \text{--- (ii)} \]
Substitute (i) into (ii):
\[ x + (2x + 6) = 36 \]
\[ 3x + 6 = 36 \]
\[ 3x = 30 \Rightarrow x = 10 \]
Substitute \(x = 10\) in (i):
\[ y = 2(10) + 6 = 26 \]
Step 4: Final Answer:
Kevin's marks = 10, Veer's marks = 26.