Alan scored a total of 14 points for answering all the 15 questions on a math quiz. For every correctly answered question, Alan got 2 points. For every wrong answer, he lost 2 points. How many questions did he answer correctly?
all correct would be 30
he's 16 points shy, so he must have missed 16/4 = 4.
11 right = 22
4 wrong = -8
22-8=14
He answered 7 correctly. You divide fourteen by two, then subtract that by fifteen. You get eight, so Alan got eight WRONG. He got seven right.
Let's assume Alan answered x questions correctly.
According to the given information, Alan answered a total of 15 questions. Therefore, the number of questions he answered incorrectly would be 15 - x.
For every correctly answered question, Alan received 2 points, so the total points earned from the correct answers would be 2x.
Similarly, for every wrong answer, Alan lost 2 points. Therefore, the points deducted for incorrect answers would be 2 * (15 - x) = 30 - 2x.
The total points that Alan scored in the quiz is given as 14.
So, combining the points earned from correct answers and the points deducted for incorrect answers, we can form an equation:
2x - (30 - 2x) = 14
Simplifying the equation:
2x - 30 + 2x = 14
Combining like terms:
4x - 30 = 14
Adding 30 to both sides:
4x = 44
Dividing both sides by 4:
x = 11
Therefore, Alan answered 11 questions correctly.
To solve this problem, we can first set up some equations based on the information given. Let's assume Alan answered x questions correctly.
Since Alan scored 2 points for every correct answer and lost 2 points for every wrong answer, we can write the equation:
2x - 2(15 - x) = 14
Simplifying the equation, we get:
2x - 30 + 2x = 14
Combining like terms:
4x - 30 = 14
Next, we isolate the variable:
4x = 14 + 30
4x = 44
Dividing both sides by 4:
x = 44/4
x = 11
Therefore, Alan answered 11 questions correctly.