On a certain test, Radeesh earned 2 points for every correct answer and lost 1 point for every incorrect answer.If he answerred all 30 questions on the test and received a score of 51, how many questions did Radeesh answer incorrectly?

Options

A. `3`
B. `7`
C. `15`
D. `21`

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define Variables
Let \( x \) be the number of correct answers that Radeesh gave. Since he answered all 30 questions, the number of incorrect answers will be \( 30 - x \).

**Hint:** Define variables to represent the quantities you are trying to find.

### Step 2: Set Up the Score Equation
Radeesh earns 2 points for each correct answer and loses 1 point for each incorrect answer. Therefore, his total score can be expressed as:
\[ \text{Total Score} = 2x - (30 - x) \]
This simplifies to:
\[ \text{Total Score} = 2x - 30 + x = 3x - 30 \]

**Hint:** Write an equation based on the scoring rules provided in the problem.

### Step 3: Set Up the Equation Based on Given Score
According to the problem, Radeesh's total score is 51. Therefore, we can set up the equation:
\[ 3x - 30 = 51 \]

**Hint:** Use the information given in the problem to form an equation.

### Step 4: Solve for \( x \)
Now, we will solve the equation for \( x \):
\[ 3x - 30 = 51 \]
Add 30 to both sides:
\[ 3x = 51 + 30 \]
\[ 3x = 81 \]
Now, divide both sides by 3:
\[ x = \frac{81}{3} = 27 \]

**Hint:** Perform algebraic operations to isolate the variable.

### Step 5: Find the Number of Incorrect Answers
Now that we have the number of correct answers \( x = 27 \), we can find the number of incorrect answers:
\[ \text{Incorrect Answers} = 30 - x = 30 - 27 = 3 \]

**Hint:** Use the total number of questions to find the remaining quantity.

### Conclusion
Radeesh answered **3 questions incorrectly**.

**Final Answer:** 3