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?
Is the answer 22????
score = 10*right - 4*wrong
s = 100 + 10r - 4w
r+w = 50
so, to get at least 350,
100 + 10r - 4(50-r) > 350
100 + 10r - 200 + 4r > 350
14r > 450
r > 32.14
so, at least 33 correct answers
100 + 32*10 - 18*4 = 348
100 + 33*10 - 17*4 = 362
To solve this problem, we will need to calculate the points earned and deducted for each correct and incorrect answer, respectively, and then determine the minimum number of questions that need to be answered correctly to have a score over 350.
First, let's calculate the points earned for each correct answer: 10 points.
Next, let's calculate the points deducted for each incorrect answer: -4 points.
Each player starts with 100 points, so let's calculate the maximum number of incorrect answers a player could give without going below 350 points:
100 - (4 * x) > 350
Here, x represents the number of incorrect answers.
Simplifying the equation:
100 - 4x > 350
-4x > 250
x < -62.5
Since we cannot have a negative number of incorrect answers, we round up to the nearest whole number (in this case, zero). Thus, the maximum number of incorrect answers is zero.
Finally, let's calculate the minimum number of correct answers needed:
50 questions - 0 incorrect answers = 50 correct answers
Therefore, the minimum number of questions a contestant must answer correctly to have a score over 350 is 50.
To summarize, the answer is NOT 22. The minimum number of questions a contestant must answer correctly to have a score over 350 is 50.