Let's break down and solve each part of this problem.

Given Information

1. Total number of questions: $110$
2. Marks for each correct answer: $+2$
3. Marks deducted for each incorrect answer: $-2$
4. Total score obtained by April: $92$

Let:

• $x$ = number of correct answers
• $y$ = number of wrong answers

Since she answered all the questions: $x + y = 110$

Part (a): How many correct answers did she have?

April’s total score can also be represented by the equation: $2x - 2y = 92$

Step 1: Simplify the equations

From $x + y = 110$, we can express $y$ in terms of $x$: $y = 110 - x$

Substitute $y = 110 - x$ into the score equation: $2x - 2(110 - x) = 92$

Step 2: Expand and solve for $x$

$2x - 220 + 2x = 92$ $4x = 312$ $x = 78$

Now, substitute $x = 78$ back into $y = 110 - x$: $y = 110 - 78 = 32$

So, April answered 78 questions correctly.

Part (b): If 112 marks were required to pass the quiz, how many more correct answers did she need to pass?

The required score is 112, so let’s find how many additional correct answers she would need.

Let $x'$ be the new number of correct answers needed to reach a score of 112: $2x' - 2(110 - x') = 112$

Following a similar approach as before: $2x' - 220 + 2x' = 112$ $4x' = 332$ $x' = 83$

Since April initially had 78 correct answers, the additional correct answers required are: $83 - 78 = 5$

Thus, April would need 5 more correct answers to pass.

Do you need further details or have any questions about this solution?

Related Questions

1. What would be April’s score if she answered 80 questions correctly and the rest incorrectly?
2. How many questions would April have to answer correctly to score exactly 100 marks?
3. If April answered 90 questions correctly, what would her total score be?
4. How many correct answers are needed to achieve a perfect score in the quiz?
5. If each wrong answer deducted 3 marks instead of 2, how would April’s score change?

Tip:

When dealing with problems involving scores or deductions, try setting up equations that account for both positive and negative contributions to the total.