In a mathematics quiz, 20 problems are given, 5 points are given for each correct answer and 2 points are deducted for each incorrect answer. Ashley scores 51 points. How many correct answers does she have?

Answer 1

11 * 5 = 11 * 5 points for each correct answer = 55

2 * 2 = 2 * 2 deducted points each incorrect answer

Formula :

11 * 5 - 2 * 2 = 55 - 4 = 51 points

11 correct answers

Answer 2

Sorry, my mistake.

x = number of correct answers

y = number of incorrect answers

x + y = 20 Subtract y to both sides

x + y - y = 20 - y

x = 20 - y

Numbers of points :

x * 5 + y * ( - 2 ) = 51

5 x - 2 y = 51

5 ( 20 - y ) - 2 y = 51

100 - 5 y - 2 y = 51

100 - 7 y = 51 Subtract 51 to both sides

100 - 51 - 7 y = 51 - 51

49 - 7 y = 0 Add 7 y to both sides

49 - 7 y + 7 y = 0 + 7 y

49 = 7 y Divide both sides by 7

49 / 7 = 7 y / 7

7 = y

y = 7

7 incorrect answers

x = 20 - y

x = 20 - 7

x = 13

13 correct answers

Number of points :

13 * 5 - 7 * 2 = 65 - 14 = 51