In a science competition with ten problems, a student gets 5 points for a correct answer and loses 2 points for an incorrect answer. If Alice answered every problem and her score was 29, how many correct answers did she have?
If there were c correct answers, then there were 10-c wrong answers. So, now use her score to find c:
5c - 2(10-c) = 29
To find out how many correct answers Alice had, we need to determine how many incorrect answers she had first.
Let's assume that Alice answered x questions correctly.
Since the competition had ten problems, the number of incorrect answers would be (10 - x).
Now, let's calculate the score for the correct answers. Alice gets 5 points for each correct answer, so she would have earned 5x points for the correct answers.
Similarly, Alice loses 2 points for each incorrect answer, which means she would have lost 2(10 - x) points for the incorrect answers.
Given that Alice's total score was 29, we can set up the equation:
5x - 2(10 - x) = 29
Now, we can solve this equation to find the value of x.
Expanding the equation:
5x - 20 + 2x = 29
Combining like terms:
7x - 20 = 29
Adding 20 to both sides of the equation:
7x = 49
Dividing both sides of the equation by 7:
x = 7
Therefore, Alice answered 7 questions correctly.