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?

Question

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????

Steve · Answer

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