alan scored a total of 14 points for answering all 15 questions on a math quiz for every correctly answered question alan got 2 points for every wrong ahe lost 2 points how many questions did he answer correclty
right: 11 = 22 points
wrong: 4 = -8 points
total: 22-8 = 14 points
To find out how many questions Alan answered correctly, we need to consider the total number of points he achieved.
Given that Alan scored a total of 14 points, we can set up an equation:
Let x be the number of questions answered correctly.
Let y be the number of questions answered incorrectly.
Each correct answer gains Alan 2 points, so Alan scored 2x points for correct answers.
Each incorrect answer deducts 2 points from Alan's score, so Alan lost 2 points for each incorrect answer, resulting in a deduction of 2y points.
Therefore, we can write the equation: 2x - 2y = 14.
However, we also know that Alan answered a total of 15 questions, so the sum of correct and incorrect answers should equal 15: x + y = 15.
Now, we can solve these two equations simultaneously. Let's use the substitution method:
From the second equation, we have y = 15 - x.
Substituting this value of y into the first equation, we get:
2x - 2(15 - x) = 14.
2x - 30 + 2x = 14.
4x - 30 = 14.
4x = 14 + 30.
4x = 44.
x = 44/4.
x = 11.
Therefore, Alan answered 11 questions correctly.