Solving X's Score Calculation Problem
This problem involves calculating the number of wrong answers given the total number of questions attempted, the marks awarded for correct answers, the marks deducted for wrong answers, and the total marks obtained.
Setting Up the Equations
Let $c$ be the number of questions answered correctly and $w$ be the number of questions answered wrongly.
We are given:
- Total questions attempted: $c + w = 94$
- Marks for each correct answer: $+4$
- Marks deducted for each wrong answer: $-1$
- Total marks obtained: $141$
The total marks can be represented as: $4c - 1w = 141$.
Calculating the Number of Wrong Answers
We have a system of two linear equations:
- $c + w = 94$
- $4c - w = 141$
From equation (1), we can express $c$ in terms of $w$: $c = 94 - w$.
Substitute this expression for $c$ into equation (2):
$4(94 - w) - w = 141$
Now, solve for $w$:
$376 - 4w - w = 141$
$376 - 5w = 141$
Rearrange the equation to isolate $w$:
$5w = 376 - 141$
$5w = 235$
$w = \frac{235}{5}$
$w = 47$
Verification
If $w = 47$, then the number of correct answers is $c = 94 - 47 = 47$.
Total marks = $(4 \times 47) - (1 \times 47) = 188 - 47 = 141$. This matches the given total marks.
Final Answer
The number of questions wrongly answered by X is 47.
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