There are 50 questions to answer in a triva contest. Each player starts with 100 points. He or she earns ten points for each correct answer but will lose four points for each incorrect answer. Each player must answer all 50 questions. What is the fewest number of questions a contestant must answer correctly to have a score over 350?
score<10*right-4(50-right)
350<right(10+4) -50
300<right(14)
solve for right
right>300/14
right>21
right=22
check all that.
To find the fewest number of questions a contestant must answer correctly to have a score over 350, we need to consider the worst-case scenario for incorrect answers. Assuming the contestant answers all 50 questions incorrectly, they would lose 4 points for each incorrect answer, resulting in a total loss of 200 points (50 incorrect answers x 4 points per incorrect answer = 200 points lost).
Since the contestant starts with 100 points, the minimum score they can have after answering all the questions incorrectly is 100 - 200 = -100.
Now, to have a score over 350, we need to find how many correct answers are required to make up for the initial score of -100 and surpass 350. The contestant earns 10 points for each correct answer, so the number of correct answers needed can be calculated as follows:
Total points required = 100 (initial score) + 10 x (number of correct answers)
For the score to exceed 350, we have the inequality:
100 + 10 x (number of correct answers) > 350
Subtracting 100 from both sides, we get:
10 x (number of correct answers) > 250
Dividing both sides by 10, we find:
number of correct answers > 25
Therefore, the contestant must answer more than 25 questions correctly to have a score over 350.