Question

There are 30 questions in a quiz. 5 marks are awarded for each correct answer n 2 marks r deducted for each incorrect answer. If Angela scores 122 marks, how many incorrect answers does she have? Step by Step, please.


Ans: 4

Answer 1

Let the Number of Correct Answers given by Angela be : C

Given : The Total Number of Questions in the Quiz = 30

★  The Number of Incorrect Answers given by Angela will be : 30 - C

Given : 5 Marks are awarded for each Correct Answer

★  The Marks Angela gets for her 'C' Correct Answers will be :

$\mathsf{\implies (5 \times C) = 5C}$

Given : 2 Marks are deducted for each Incorrect Answer

★  Marks which get deducted for (30 - C) Incorrect Answers will be :

$\mathsf{\implies 2 \times (30 - C) = 60 - 2C}$

Given : Total Marks scored by Angela = 122

★  The Difference of Marks scored for Correct Answers and Marks deducted for Incorrect Answers should be equal to 122

$\mathsf{\implies 5C - (60 - 2C) = 122}$

$\mathsf{\implies 5C - 60 + 2C = 122}$

$\implies \mathsf{7C = 122 + 60}$

$\implies \mathsf{7C = 182}$

$\implies \mathsf{C = \dfrac{182}{7}}$

$\implies \mathsf{C = 26}$

★  Number of Correct Answers given by Angela = 26

★  Number of Incorrect Answers given by Angela = (30 - 26) = 4

Answer 2

Answer: 4 wrong answers( I used Solve by assuming method because it is easier for me to do)

Step-by-step explanation:

total=30 questions

Angela's score=122 marks

Assume all of her answers are correct:

30×5=150 marks

150-122marks=28marks

Given: 5 marks are awarded for each correct answer n 2 marks r deducted for each incorrect answer

So, 5+2=7marks

Therefore, 28÷7=4 wrong answers

Please mark me as brainliest.