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?
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
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
Let's assume that Ashley answered x questions correctly.
Since each correct answer gives her 5 points, the total points she earns from correct answers is 5x.
Since each incorrect answer deducts 2 points, the total points deducted for incorrect answers is 2(20 - x) = 40 - 2x.
Given that Ashley's total score is 51, we can set up the equation:
5x - (40 - 2x) = 51.
Simplifying the equation, we get:
5x - 40 + 2x = 51.
Combining like terms, we have:
7x - 40 = 51.
Adding 40 to both sides of the equation, we get:
7x = 91.
Dividing both sides of the equation by 7, we get:
x = 13.
Therefore, Ashley answered 13 questions correctly.
To find out how many correct answers Ashley has, we can set up an equation using the given information.
Let's say Ashley answered "x" questions correctly.
Since she answered 20 problems in total, the number of incorrect answers would be 20 - x.
According to the scoring system, each correct answer earns 5 points, so the total points Ashley earned from correct answers would be 5x.
And each incorrect answer deducts 2 points, so the total points Ashley lost from incorrect answers would be 2(20 - x).
Given that Ashley scored 51 points in total, we can set up an equation:
5x - 2(20 - x) = 51
Now let's solve this equation to find the value of x, which represents the number of correct answers Ashley has.
5x - 40 + 2x = 51
Combining like terms:
7x - 40 = 51
Add 40 to both sides:
7x = 91
Divide both sides by 7:
x = 13
Therefore, Ashley answered 13 questions correctly.